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:

• 3Πu Spin = 1; projection of the angular momentum Λ = 1; wavefunction changes sign on inversion (u)
• 1Σ+ Spin = 0; projection of the angular momentum Λ = 0; sign of wavefunction remains unchanged on reflection on a plane which contains both nuclei (+). It is a heteronuclear molecule (no g or u)

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