28_580ln_fa08

# 28_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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5.76 Lecture #2 8 Page 1 of 8 pages Lecture #2 8 : Polyatomic Vibrations IV: Symmetry What is a normal mode? all atoms undergoing oscillation at the same frequency and phase and with amplitudes determined by the eigenvectors of the GF matrix. = L 1 s t α = s t α (t) e ˆ s t α Q S we built in specific relative lengths s t α (t) cos ( λ t + δ ) of displacements -1 S i eigenvectors are e.g. Q j = L ji rows of L –1 i If we represent S i by a set of s i α vectors of prescribed lengths and directions, then L –1 tells us how to weight and add the vectors at each atom associated with the various internal displacements e.g. H 2 O (page 4 of H 2 O example in 4/24/96 notes) Q 1 = 0.685 (S 2 – S 1 ) Q 2 = 0.695 (S 1 + S 2 ) + 0.037S 3 Q 3 = 0.655S 3 S 1 = S 2 = S 3 =
5.76 Lecture #2 8 Page 2 of 8 pages Q 1 = = Q 2 = = Q 3 = names of normal modes from pictures or from equations? Note that each of the pictures involves some change of bond angle. So which mode is the “bend”? Q 1 involves dominantly a compression of one bond and an expansion of the other equivalent one; Q 2 involves dominantly two equivalent bonds expanding and contracting in phase; Q 3 pure internal bend. equations : S 1 ± S 2 “symmetric” “antisymmetric” mixed character — no S 3 in Q 1 some S 3 character in Q 2 Why no (S 1 + S 2 ) character in Q 3 ? Actually, there is some, but very small.

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5.76 Lecture #2 8 Page 3 of 8 pages NON-LECTURE 0.041 0.041 0.000 0.001 1.529
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28_580ln_fa08 - MIT OpenCourseWare http/ocw.mit.edu 5.80...

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