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12_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 #12 Fall, 2008 Page 1 of 12 pages Lecture #12: Rotational Assignment of Diatomic Electronic Spectra I Difficult to establish absolute rotational assignment of real electronic bonds because * band heads - not all rotational lines are resolved * zero-gap is obscured * overlap by other bands and atomic lines * imperfections such as “perturbations” and “Predissociation” See Herzberg Diatomics, pp. 168-192 TODAY 1. Nothing known at the start. The Fortrat Parabola - R and P branches fit one parabola but with arbitrary numbering! How do we decide on correct numbering? 2. B-value for 1 or 2 states known one known set of rotational combination differences 2 F(J) “LAGERQVIST STRIP” 3. Nothing known. Simultaneous analysis of two bands that the vibrational analysis suggests share a vibrational level in common. Tedius trial and error method. Z unknown 4. Computer automated analysis of B known A based on known 2 F(J)’s and intensity systematics 5. Loomis-Wood plots: picking out branches (fragmentary patterns) 6. Laser Excited Dispersed Fluorescence (DF) spectrum Grating spectrograph ~24 Glass Plate, 10µ slit 600mm 10 –2 mm = 6 × 10 4 resolution elements typically ~10 3 rotational lines in a sense all 10 3 lines must be simultaneously assigned * several complex decisions, all made correctly * enormous redundancy pattern recognition supplemented by trial and error Figure 1 a trivial spectrum (SiO), assignable just like a vibration-rotation band in IR Figure 2 non-trivial. Same molecule. same electronic system. “IMPERFECTIONS”
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5.80 Lecture #12 Fall, 2008 Page 2 of 12 pages overlap perturbations impurities (SiO + , SiN) Image of a trivial spectrum (SiO), assignable just like a vibration-rotation band in IR removed due to copyright restrictions. Figure 1 Image of a non-trivial. Same molecule. Same electronic system. "Imperfections" removed due to copyright restrictions. Figure 2 Fortrat parabola - one equation accounts for both R and P branches of 1 + 1 + system. B ν (n) = ν 0 + (B + B )n + (B – B )n 2 origin linear quadratic P(J) = ν (–J) i.e. n = –J R(J) = ν (J + 1) i.e. n = J + 1 relativism - any numbering is possible — same parabola, but apparently different equation. i.e. let m = n + 2. Then we get ν (m) = [ ν 0 2(B + B ′′ + 4 B ] + [ B + B ′′− 2 B ] + Bm 2 new origin term new linear same quadratic term )
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5.80 Lecture #12 Fall, 2008 Page 3 of 12 pages Image removed due to copyright restrictions. Please see: Fig. 24 in Herzberg, G. Spectra of Diatomic Molecules . New York, NY: Van Nostrand, 1950. Figure 3 Image removed due to copyright restrictions.
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