correctedC566lecture25

correctedC566lecture25 - C566 Master Lecture Notes Lecture...

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1 C566 Master Lecture Notes Lecture 25 Forbidden Transitions- observed via (2) Breakdown of the Born-Oppenheimer approximation BO approx says that the description of the electronic wavefunction can be separated from the vibrational wavefunctions. BO: = el ( q ; Q K,0 ) vib ( Q i ) Relax Q 0 : el = el ( q , Q i ) 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 Therefore, dipole allowed transitions can be made only to A 2u or E 1u (green) electronic states. b 2g e 1g e 2u a 2u
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Given that the B 1u + B 2u + E 1u states originate from the same electronic orbital occupancy, they can couple. 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 So this looks just like perturbation theory, in which = 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 we truncate contributions from 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 So for the S
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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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correctedC566lecture25 - C566 Master Lecture Notes Lecture...

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