24_580ln_fa08

24_580ln_fa08 - MIT OpenCourseWare http:/ocw.mit.edu 5.80...

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MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.80 Lecture #24 Fall, 2008 Page 1 of 7 pages Lecture #24: Pure Rotation Spectra of Polyatomic Molecules Last time: Asymmetric tops A B C B K 2 H ROT BJ(J + 1) + JK JK = B C A B 1 [ (J K)(J K 1)(J ± K + 2)(J ± K + 1) ] 1/2 JK JK ± 2 4 + asymmetry parameter κ ≡ 2B – A – C prolate B = C κ = –1 A – C oblate A = B κ = +1 A + C most asymmetric B = 2 κ = 0 Perturbation Theory: H JK,JK ± 2 1 f(J,K) = E ° κ Factor H ROT into four blocks — can label these blocks according to whether K p and K o (or K a and K c ) are even or odd e,e e,o o,e o,o correspond to rotational symmetry species — good quantum numbers [not related to geometric symmetry operations applied to rigid molecule]. TODAY pure rotation spectra SYMMETRIC TOP M x = M y = 0, K = 0 like diatomic. Only get information about B from pure rotation spectrum.  ASYMMETRIC TOP M can have 1, 2, or 3 non-zero components Transition K p K o a-type even odd b-type odd odd c-type odd even NOTATION/ASSIGNMENT v i Ω f J f M f P if ε S M b,if ( Q ) v f Ω i J i M i α Sb S,b pure Hougen, p. 31 rotation f(J i ,J f )g(J i i ;J f f )h(J i M i ;J f M f body lab M b (Q e ) polarization polarization 2
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5.80 Lecture #24 Fall, 2008 Page 2 of 7 pages BODY COMPONENT b (a, b, or c) K Symmetric Tops - can’t have nonzero dipole to unique axis: z z a prolate if there were a µ component, it would z c oblate have to point in same direction after a “parallel” type transitions only C n (z) or S n (z) operation. µ = 0 for n 2. K = 0,
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24_580ln_fa08 - MIT OpenCourseWare http:/ocw.mit.edu 5.80...

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