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Unformatted text preview: 09Feb2011 Chemistry 21b Spectroscopy Lecture # 16 Local Mode Theory & The Vibrations of Functional Groups Despite the general success of normal mode theory in the analysis of polyatomic molecule vibrational spectra, there are several experiments that are difficult to explain if molecules truly behave as point masses coupled by harmonic springs. Some of the more perplexing of these include: I. IR Multiphoton Dissociation (MPD) In these experiments, molecules are subject to intense mid-IR radiation fields (typically from a CO 2 laser), and are found to fall apart. If normal modes really did not couple to each other we might consider that each vibrational motion could be represented by states in some kind of anharmonic effective potential. The precludes IR MPD because after one photon is absorbed, the second absorption event which allows the molecule to climb the well can no longer occur on resonance. For instance, a CO 2 laser at 1000 cm 1 is resonant with an asymmetric stretching motion of SF 6 . If the anharmonicity is 1%, then 1 1000 cm 1 , 1 2 990 cm 1 , 2 3 980 cm 1 , . . .; and the line width of the laser is 1 MHz. To get 20 cm 1 of power broadening (that is, to generate 20 cm 1 Rabi frequencies), a laser fluence in the MW/cm 2 range is needed, much below those at which IR MPD is found to occur. For example, the IR MPD of (C 2 H 5 ) 2 OH + occurs at 1 W/cm 2 (Beauchamp et al., JACS 100 , 3248(1978))! How could we possibly climb the ladder? How can the molecule ever absorb enough energy? After all, several eV are required, but h CO 2 . 1 eV. Could it be dielectric breakdown, that is a transition from discrete quantum states to a pseudo-continuous classical dielectric continuum? Nope! The process is isotope selective (for example, there have been proposals that IR MPD of UF 6 can be used to separate 235 U and 238 U; Bloembergen, Opt. Commun. 15 , 416(1975)). How does this model disagree with our intuition about quantum mechanics, and how should we think about the steady state picture breaking down? Think for a moment what is true about eigenstates: (1) When energy level spacings become less than the natural line widths the eigenstates dont really exist (e.g. a baseball in a macroscopic box can be thought about classically). (2) Perhaps the radiation does not carry intensity to an eigenstate, but will carry intensity to a coherent superposition (we wont have a lot to say about this, but it is essential to much of time resolved, or ultrafast, laser studies). Other disturbing experiments: II. IR Fluorescence If the asymmetric stretch of SF 6 is excited at 10 m with a CO 2 laser, fluorescence from a bending state is observed at 15 m (Manucia, Chem. Phys. Lett. 54 , 451(1978))....
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