11_580ln_fa08

11_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 #11 Fall, 2008 Page 1 Lecture #11: Pictures of Spectra and Notation Last Time Selection, propensity and intensity rules  M(R) if α Sb ( θ , φ ) Ω i Ω f absolute rotational linestrengths S J i J f  permanent Sum rule rotation dipole P µ 2 g i or S 2 typical form for universal angular dM vibration dM P dQ vg i dQ factor must sum to 1 or to electronic M if v i | v f P M 2 q v i v f g i TODAY: Patterns in spectra Typical constants How to assign spectra - problems and tricks Notation PURE ROTATION total degeneracy µ-wave sources limit range of J sampled (more difficult to assign than expected) superposition of lines from vastly different energy regions, isotopomers population effects. How to tell up from down. Think about this! VIBRATION-ROTATION J range limited by T, not by radiation source. P and R branch structure - open, no heads, zero gap (easy to assign) PQR notation hot bands and isotopomers ELECTRONIC Band heads due to large | B | blue vs. red degraded sign of B (hard to assign because of overlapping lines) J Head vibrational Sequences vs. Progressions Qualitative Franck-Condon Principle Universal notation for all molecular spectroscopy. Upper level denoted by always stated first Lower level denoted by always stated second
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5.80 Lecture #11 Fall, 2008 Page 2 Z Z – Z (for any quantity, Z) J = J – J O – 2 P – 1 Q 0 i.e. R(J) means R 1 S 2 Denote whether transition is absorption or emission by direction of arrow. Always state upper level first. PURE ROTATION SPECTRA – µ-wave (e.g. heteronuclear diatomic) requires permanent dipole moment ν 10-300 GHz [ ν = ν /c c = 3 × 10 10 cm/s] λ 3cm – 1mm “cm-wave” and “mm-wave” regions ΩΩ for 1 + J = ±1 only because = 0. recall S J i J f J J + 1 J 2 (J + 1) 2 (J) – F v (J – 1) = 2JB v – 4J 3 D v centrifugal distortion
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11_580ln_fa08 - MIT OpenCourseWare http:/ocw.mit.edu 5.80...

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