Term symbols

The term symbol for the total electronic configuration depends on the occupied electronic states. Full states have A-Symmetry, i.e. they are totally symmetric and need no further consideration. Partially occupied states are subject to multiplication as described in the chapter product rules.

Ci Ag Au Ag Ag Au Au Au Ag		Cs A' A'' A' A' A'' A'' A'' A'
C2 A B A A B B B A	C2h A1 A2 A1 A1 A2 A2 A2 A1	C2v A1 A2 B1 B2 A1 A1 A2 B1 B2 A2 A2 A1 B2 B1 B1 B1 B2 A1 A2 B2 B2 B1 A2 A1

Examples for the determination of the total electronic configuration

C_s:    One electron occupies an a', a second an a" state:

(a')¹ (a'')¹ yields configuration a' x a''  =  a''  ≡  A''

If the spin is antiparallel, the result is the singlett state ¹A'', otherwise triplett state ³A''.

C_2v:   Two electrons are in state b₂ (e.g. H₂O)

(b₂)²  →   b₂ x b₂  =  a₁  ≡   A₁  →   ¹A₁

Alternatively, if one electron is in state b₂ and the other in a₁ as in an excited state of the water molecule, two possible total electronic configurations result.

(b₂)¹ (a₁)¹  →  b₂ x a₁  =  b₂  =  B₂    → ¹B₂ or ³B₂

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