Molecular term sybol

Molecular term symbol

1. SAJAD AHMAD SHEER GUJRI 16062120033 KASHMIR UNIVERSITY [phone] DEPTT . OF CHEMISTRY UNIVERSITY OF KASHMIR Topic: Molecular term symbol 1

2. Introduction 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. 2

3. 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. 3

4. Symmetries of diatomic molecules In group theory, heteronuclear diatomic molecules have C ∞v symmetries, and homonuclear ones have D ∞h symmetries. There are infinitely many representations in both groups, among which the irreducible representations are symbolized using the notations "Σ, Π, Δ, etc. Both kinds of groups bear a perpendicular mirror plane, or σ v . So (+) and (-) are used to categorize the symmetry with respect to σ v . D ∞h symmetries indicate an inversion center in the molecule, yet C ∞v symmetries do not. For D ∞h , irreducible representations are further classified by parity, using the " g " and " u " symbols. 4

5. For homonuclear diatomics, the term symbol has the following form: 2S+1 Λ (+/−) Ω, ( g/u) 5

6. whereas Λ is the projection of the orbital angular momentum along the internuclear axis. And Λ may be one of the greek letters in the sequence: Σ Π Δ Φ ... when Λ = 0, 1, 2, 3 ..., respectively. Ω is the projection of the total angular momentum along the internuclear axis. the g/u subscript applies only to molecules with a Centre of symmetry and labels the symmetry of the electronic wave function with respect to inversion through this Centre; the +/− superscript applies only to Σ states, and labels the symmetry of the electronic wave function with respect to reflection in a plane containing the nuclei. For heteronuclear diatomics, the term symbol does not include the g/u part, for there is not inversion center in the molecule. 6

7. MOLECULAR ORBITAL One electron O.A.M along inter-nuclear axis ML = ∑ml Λ Term Symbol ml (or λ) = ∑λ σ ∑ π ±1 ±1 1 ∏ δ ±2 ±2 2 ∆ 7

8. Some important points If the symbol is Σ then (+) and (-) super script are used. g and u is reffered to the orbital of last electron filled. When wave function does not change sign under reflection then (+) sign is used. When wave function changes sign under reflection then(-) sign is used. If electrons lies in different orbital then g×g = g g×u = u u×u = g 8

9. Selection Rules : 1. ΔΛ = 0, ±1 Transitions such as Σ ̶ Σ, Π ̶ Σ, Π ̶ Π, Δ ̶ Π are allowed. Transitions such as Δ ̶ Σ, and Φ ̶ Π are not allowed. 2 . ΔS = 0, transitions allowed such as 3 Π ̶ 1 Σ + , are not allowed. 3. ΔΩ = 0, ±1 4.g →u, u→g are allowed, but g→g and u→u are not allowed . 5. Transitions like + ↔ - are not allowed, but +↔ + and - ↔ - are allowed 9

10. Examples : H 2 molecule Ground state: ( 1 σ g 2 ) ML=0 , Λ= MS =0, S=0, both electrons are in gerade Term = 1 Σ g + 10

11. For O 2 molecule: Ground state : ( 1 σ g ) 2 ,(1 σ* u ) 2 ,(2 σ g ) 2 ,(2 σ* u ) 2 ,(3 σ g ) 2 ,(1 π u ) 2 ,(1 π u ) 2 ,(1 π* g ) 1 ,(1 π* g ) 1 ML =0 Λ = S =1 2S+1 =3 +1 -1 two electrons are are present in two diff. orbitals i;e g×g =g Complete term = 3 Σ g - 11

12. Excited states of o 2 +1 -1 +1 -1 or or +1 -1 +1 -1 Λ = +1-1 =0 Λ = |±2| = 2 2s+1 = 1 2s+1 = 1 1 Σ g + 1 Δ g 12

13. Energy ordering: Hund’s rules are a useful guide to the energy ordering of terms arising from the ground state electron configuration : The term with the highest spin multiplicity, 2S + 1, is lowest in energy. For terms of the same multiplicity, the term with the largest orbital angular momentum, given by Λ, is lowest in energy. For example, the terms arising from the ground state of O 2 lie in the order 3 Σ − g , 1 ∆ g , 1 Σ + g 13

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