C566lecture25_000

C566lecture25_000 - C566 Master Lecture Notes Lecture 25...

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1 C566 Master Lecture Notes Lecture 25 REMINDERS: Midterm 2 will be on 19 April, 2011 during class CCJ traveling 17-19 April, so no office hour on 18 April Don’t forget- final paper due during finals week (noon on Tuesday, 3 May). Forbidden Transitions- observed via (2) Breakdown of the Born-Oppenheimer approximation BO: = el ( q i ; Q K,0 ) vib ( Q i ) Relax Q 0 : el = el ( q i , Q K ) Example again: BENZENE Ground State Excited states frp, * S 0 ( S 1 , S 2 ?) (S 0 ) = A 1g (S ? ) = e 1g e 2u = B 1u + B 2u + E 1u (S 1 , S 3 , S 4 ) (S 2 ) = e 1g b 2g = E 2g (x) = E 1u (y) = E 1u (z) = A 2u b 2g e 1g e 2u a 2u
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2 Consider : e 1g e 2u = B 1u + B 2u + E 1u Coupling between states with same orbital occupancy? S1 = a S1 0 + b S3 0 (a 2 + b 2 = 1) big small M e =  S1 | e | S0 = a  S1 0 | e | S0 + b  S3 | e | S0 Zero small, but non-zero Perturbation theory: = a n n o + n i o i i Ψ a H = H o + H S 1 = a S 1 0 + b S 3 0 H = H el = (H el ) 0 + i i i e Q Q H 0 +HOT B.O. breakdown T e r m t e r m Truncate at states that will not matter (e.g., other forbidden states, states that are much higher in energy). Easy for 1 o , harder for higher orders Nuclear motion mixes the electronic states Forbidden states mix with allowed states Forbidden state borrows or steals intensity form the allowed state Sticking with perturbation theory formulation: 0 0 0 0 0 | | j i ij i j i i E H So for our benzene: 0 3 0 1 3 0 1 0 0 3 0 1 1 | ) ( | S E S Q Q H S S S S S i el i So for the S 1 S 0 transition
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3 M el = S 1 | e |S 0 + 0 1 3 0 1
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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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C566lecture25_000 - C566 Master Lecture Notes Lecture 25...

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