MO Diagram from Group Theory: Central Atom

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SUMMARY

The discussion focuses on determining the central atom's orbitals using point group character tables in group theory, specifically for the carbonate ion CO3^-2 with the D3h symmetry. The central atom, carbon, has its p-orbitals represented by the symmetry labels a1'' and e', while the s-orbital is denoted as a1'. The participants express uncertainty about the derivation of these orbital representations from the character table and seek further resources for clarification.

PREREQUISITES
  • Understanding of group theory and symmetry in chemistry
  • Familiarity with point group character tables
  • Knowledge of Mulliken symmetry symbols
  • Basic concepts of molecular orbital theory
NEXT STEPS
  • Research how to interpret point group character tables in molecular symmetry
  • Study the significance of Mulliken symbols in molecular orbital theory
  • Explore the application of group theory in predicting molecular shapes
  • Learn about the D3h point group and its implications for molecular orbitals
USEFUL FOR

Chemistry students, particularly those studying molecular symmetry and group theory, as well as researchers involved in computational chemistry and molecular modeling.

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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