# 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-1π

^{2}u 1π

^{2}u

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_{g}2p

_{z})

^{2}(π

_{u}2p)

^{4}(π

^{*}

_{g}2p)

^{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},

^{1}Δ

_{g},

^{3}Δ

_{g}

### Q. Calculate the term symbol of H_{2}^{+}

Answer: Term Symbol = ^{2}∑

^{+}

_{g}

### Q. Calculate the term symbol of NO

Answer: Term Symbol =^{2}π

_{g}

**CSIR NET/JRF June 2011**

### Calculate the term symbol of a molecule with electronic configuration (1σ^{2}_{g})(1σ^{2}_{u})(2σ^{2}_{g})(2σ^{2}_{u})(1π_{u})^{1}(1π_{u})^{1}

Answer: Term Symbol = ^{3}∑

^{−}

_{g}