Term symbol of homopolar molecules

Given the electronic configuration of a molecule, we can define its term symbol as follows:

Where:

  • indicates the value of the total spin;
  • is the symbol that represents the eigenvalue of , fixed by the value of ;
  • , from the German gerade (even) or ungerade (odd), indicates whether the molecule has a defined parity with respect to its centre;
  • indicates the rotational symmetry within respect to a molecular plane: we use when the molecule is symmetrical, when it's not.

Values of has to be chosen according to these rules, in analogy with atomic orbitals:

MLtot Λ
0 Σ
1 Π
2 Δ
3 Φ

As for atomic orbitals, in a diatomic molecule we can have two electrons in the orbital, in the orbital six due to the three-fold degeneracy and so on. In the molecular case however, the energy disposition of the molecular orbitals is non trivial, but it has to be derived from case to case.

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