Molecular Term Symbol

Molecular Term Symbol

Molecular term symbols mark different electronic energy levels of a diatomic molecule. These symbols are similar to atomic term symbols, since both follow the Russell-Saunders coupling scheme. Molecular term symbols employ symmetry labels from group theory. The possibility of an electronic transition can be deducted from molecular term symbols following selection rules. For multi-atomic molecules, symmetry labels play most of term symbols' roles. Molecular Term Symbol Representation-


Up to Nitrogen molecule-


After Nitrogen molecule-


Spectroscopic Symbol-

Λ → L →	0	1	2	3
Symbol	∑	π	Δ	ϕ

Rules for g / u
g x g = g
g x u = u
u x u = g
u x g = u

If last electrons are in σ and π^*, the parity is 'g'
If last electrons are in π and σ^*, the parity is 'u'


Rules for + / −
(+) x (+) = (+)
(+) x (−) = (−)
(−) x (−) = (+)
(−) x (+) = (−)

Example-

Q. Calculate the Term Symbol of Nitrogen molecule

Configuration of Nitrogen-
1π²u 1π²u



Λ → L → = 0
Spectroscopic symbol = ∑
Spin multiplicity (2S + 1) = (2 x 0 + 1) = 1
both electrons are in 'u'
so, u x u = g
u x u = g
g x g = g
Two electrons are in p_x
i.e. (+) x (+) = (+)

Two electrons are in p_y
(−) x (−) = (+)
so, (+) x (+) = (+)
Now the term symbol-
¹∑⁺_g

Q. Calculate the Term Symbol of Oxygen molecule

kk: (σ_g2p_z)² (π_u2p)⁴ (π^*_g2p)²

Λ = L = 0 + 0 + 1 + 1 − 1 − 1 + 1 − 1 = 0
Spectroscopic Symbol = ∑
Last electrons are in 'g'
so, g x g = g
Symbol = ∑_g

One electron is in +ve and one electron is in −ve with same spin-
(+) x (−) = −
Symbol = ∑⁻_g
Spin multiplicity (2S + 1) = (2 x 2/2 + 1) = 3
so, Term Symbol = ³∑⁻_g
Similarly, calculate other term symbols, if configuration changed.
Other Term Symbol = ³∑⁺_g, ¹Δ_g, ³Δ_g

Q. Calculate the term symbol of H₂⁺

Answer: Term Symbol = ²∑⁺_g

Q. Calculate the term symbol of NO

Answer: Term Symbol = ²π_g

CSIR NET/JRF June 2011

Calculate the term symbol of a molecule with electronic configuration (1σ²_g)(1σ²_u)(2σ²_g)(2σ²_u)(1π_u)¹(1π_u)¹

Answer: Term Symbol = ³∑⁻_g