Spectroscopic Notation for Linear Molecules

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	+,−
	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. λ_d = ± 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:

³Π_u 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.