C566lecture21_000

C566lecture21_000 - C566 Master Lecture Notes Lecture 21...

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1 C566 Master Lecture Notes Lecture 21 Several real-case examples of spin-orbit splitting in doublet and triplet states, to be discussed in class:
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3 Electronic Spectroscopy of Polyatomics See sec. 6.3 in Hollas Heirarchy of Problems in Electronic Spectra Symmetry and identity of electronic states Symmetry selection rules experimatal data for calculations FC and vibrational activity Q i and i Rotational structure of vibratinoal bands moments of inertia, identity of the excited state Perturbations (galore) o Forbidden electronic transitions o Mixed vibrational states o Mixed vibrational-rotational states Selection Rules for Electronic Transitions As always, approximate: = el vib rot spin Ignore the rotational portion for now- Again, it involves the orientation of the whole molecule in the field of the photon. P f-i |  f | x,y,z | i | 2 = M x 2 + M y 2 + M z 2 By comparing SO splittings in Si 2 , Ge 2 and Sn 2 triplet neutral states, we can see a progression from Hund’s cases a and b down to Hund’s case c. In Sn 2 , the 2 u -1 u splitting is singnificantly compressed via “repulsion” between what would nominally be described as a 3 1,u SO component with the higher-lying 1 1,u state
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4 As with diatomics, = Z K e R K e r j = n + el K indexes the nuclei R K is their position j indexes the electrons r j is their position Can resolve = ( x , y , z ) = ( n,x + el,x , n,y + el,y , n,z + el,z ) M x =  mol | n,x | mol  +  mol | el,x | mol  =  el | el   vib (Q i ) | n,x | vib (Q i )  spin | spin  +  el | el,x | el   vib (Q i )| vib (Q i )   spin | spin  | = (transition dipole integral) vib overlap integras [ S = 0] (neglecting rotations
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This note was uploaded on 01/18/2012 for the course C 566 taught by Professor Carolinechickjarroll during the Spring '11 term at Indiana.

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C566lecture21_000 - C566 Master Lecture Notes Lecture 21...

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