Spectroscopic notation
for linear molecules (C∞v)


2S+1
Multiplicity; from the resulting total spin S of each electron spin

Example:
2 electrons can combine to
↑↓  S = +½ − ½ = 0 => 2S + 1 = 1 (singlet)
↑↑  S = +½ +½ = 1  => 2S + 1 = 3 (triplet)

+,−
Symmetry of the wavefunction with respect to reflection on a plane which contains both nuclei.

not:

For Π, Δ, Φ ... always both + and − exist. Thus, only &Sigma states are classified. (The - sign is only possible for a combination of π, δ,... orbitals.) 

2S+1
Λ
+,−

Ω(g,u)

Λ
Projection of the orbital angular momentum (of the electrons) on the internuclear axis; classified according to Greek letters: 
 0 ≡ Σ, 1 ≡ Π, 2 ≡ Δ, 3 ≡ Φ,...

A π resp. a δ electron (projection λ π = ± 1, resp. λd = ± 2) combine to
  Λ = 2 − 1 = 1 => Π state
  Λ = 2 + 1 = 3  => Φ state
Since (−2 +1) resp. (−2 −1) are also possible, each state is degenerated twofold.

Ω
Ω = Λ+Σ
2Π state (Λ =1) and spin S=½ yields
Λ = 1+½ =3/2 and Λ = 1-½ =1/2
g,u
Symmetry of the wavefunction with respect to inversion. Only possible for homonuclear molecules

: g gerade, because sign remains unchanged

: u ungerade, because sign changes


Examples:

Auf diesem Webangebot gilt die Datenschutzerklärung der TU Braunschweig mit Ausnahme der Abschnitte VI, VII und VIII.