C566lecture19_000

C566lecture19_000 - C566 Master Lecture Notes Lecture 19...

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1 C566 Master Lecture Notes Lecture 19 Second look at FCF’s: Ground vibrational level of the X state can be expressed as a superposition of the excited states.  (0) = c o  (0) + c 1  (1)+ c 2  (2)+ c 3  (3)+ c 4  (4) + … From normalization, |c i | 2 = 1 FCF 0-0 = |<  (0)|  (0)>| 2 = |<  (0)| c o  (0) + c 1  (1)+ c 2  (2)+ c 3  (3)+ c 4  (4) + …>| 2 = | c 0 | 2 + a bunch of zeros. FCF 1 0 =|<  (1)|  (0)>| 2 = |<  (1)| c o  (0) + c 1  (1)+ c 2  (2)+ c 3  (3)+ c 4  (4) + …>| 2 = 0 + |c 1 | 2 + a bunch of zeros. FCF’s give the square modulus of the projection of an initial state vibrational wavefunction onto the excited state wavefunctions FCF’s = 1. Tools of the vibrationally-resolved electronic spectroscopy trade: Transition energy = E = E el + E vib = [E el E el ] + {[ e (  + ½ ) e x e (  + ½) 2 ] [ e (  + ½) e x e (  + ½) 2 ]} Deslandres Tables:   = 0 1 2 3 4 5 6 7 8 0 Origin of spectrum, T o T o e + 2 e x e T o 2 e + 4 e x e E t c 1 T o +  e 2 e x e T o +  e 2 e x e  e + 2 e x e 2 T o + 2  e 4 e x e Etc. 3 T o + 3  e 6 e x e 4 T o + 4  e 8 e x e 5 Etc. 6
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2 Organization of the peaks in these tables allows facile analysis of vibrational energy levels in both electronic states in question Below is data from an electronic transition in CO. Frank Condon Integals
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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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C566lecture19_000 - C566 Master Lecture Notes Lecture 19...

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