# Term symbol of homopolar molecules

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

${\displaystyle ^{2S+1}\Lambda _{u/g}^{\pm }}$

Where:

• ${\displaystyle S}$ indicates the value of the total spin;
• ${\displaystyle \Lambda }$ is the symbol that represents the eigenvalue of ${\displaystyle L_{z}}$, fixed by the value of ${\displaystyle M_{L}^{tot}}$;
• ${\displaystyle g/u}$, from the German gerade (even) or ungerade (odd), indicates whether the molecule has a defined parity with respect to its centre;
• ${\displaystyle \pm }$ indicates the rotational symmetry within respect to a molecular plane: we use ${\displaystyle +}$ when the molecule is symmetrical, ${\displaystyle -}$ when it's not.

Values of ${\displaystyle \Lambda }$ 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 ${\displaystyle \Sigma }$ orbital, in the ${\displaystyle \Pi }$ 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.