18_580ln_fa08

18_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 #18 Fall, 2008 Page 1 of 9 pages Lecture #18: Perturbations Last time: pattern forming rotational quantum numbers give * 1 + -like pattern * natural grouping of several nearly identical patterns * coupling terms that give systematic departure from one limiting case e.g. S-uncoupling in Λ -S multiplet -uncoupling in Rydberg complex (“pure precession”) Today: “Accidental” departures from regular pattern * level spacings * intensities due to accidental degeneracy between zero-order states. Avoided crossings on term value plots Disruption of spectrum - lines out of order, extra lines Railroad tie diagrams for perturbations - importance of e and f rather than + and – labels 2 × 2 degenerate perturbation theory secular equation. trace invariance intensities Suppose there are 2 electronic states near each other. If they have different ω e and B e values, there will be many intersections of the rotational term value plots. Always H , J 2 = 0 J is a rigorous quantum number. No J 0 matrix elements of H . v p v m + 1 v m term value plot (m = main “bright” p = perturber “dark”) E J 0 (m) J 0 (m + 1) B p > B m J(J + 1) What happens to spectrum for levels near curve crossings?
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5.80 Lecture #18 Fall, 2008 Page 2 of 9 pages Born-Oppenheimer breakdown effects: * avoided crossing * level repulsion * mixing * extra lines * intensity borrowing * a perturbation * interference effects-subtle (anomalous R:P intensity ratios) Spectra get complicated and difficult to assign because patterns get distrupted.
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

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18_580ln_fa08 - MIT OpenCourseWare http:/ocw.mit.edu 5.80...

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