Chem120A+Notes+10-24-08 - Chem120A Notes 10/24/08 Atomic...

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Chem120A Notes 10/24/08 Atomic Selection Rules ( 1 ) 1 , 0 , 1 ± = Δ ± = Δ J L except for for 0 0 transitions is forbidden 0 = Δ J 2 P 2 S = Δ L 1 allowed 2 S 2 D = Δ L 1 not allowed 2 F 2 P = Δ L 1 not allowed Atoms j j j jjj ij ij j i r r r r Z H v l v v + + = ∑∑ > ) ( 1 2 1 ˆ 2 ξ ( 2 ) Where the last term in (2) comes from spin-orbit coupling spin-orbit coupling is a relativistic contribution to Hamilton this is a small contribution, which is only important when atomic number is large j l v electronic orbital angular momentum of electron j j s v spin angular momentum of electron j i scalar function of j r v There are several (6 to 7) more relativistic contributions we can make to the Hamiltonian Molecules α, β for nuclei i, j for electrons > > + + + = i ij i i i i r r Z r Z Z M H 1 2 1 1 2 1 ˆ 2 2 α αα β αβ βα (3) In (3), the 1 st term is for nuclear kinetic energy, 2 nd term is for electron kinetic energy, 3 rd term is
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Chem120A+Notes+10-24-08 - Chem120A Notes 10/24/08 Atomic...

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