Electronic-vibrational-rotational spectroscopy

Bom-Oppenheimer approximation (p. 229) potential energy curve (p. 231) potential energy (hyper)surface (p. 233) electronic-vibrational-rotational spectroscopy (p. 235) non-bound states (p. 247) non-bound metastable states (p. 247) wave function measurement (p. 251)... 

While a laser beam can be used for traditional absorption spectroscopy by measuring / and 7q, the strength of laser spectroscopy lies in more specialized experiments which often do not lend themselves to such measurements. Other techniques are connnonly used to detect the absorption of light from the laser beam. A coimnon one is to observe fluorescence excited by the laser. The total fluorescence produced is nonnally proportional to the amount of light absorbed. It can be used as a measurement of concentration to detect species present in extremely small amounts. Or a measurement of the fluorescence intensity as the laser frequency is scaimed can give an absorption spectrum. This may allow much higher resolution than is easily obtained with a traditional absorption spectrometer. In other experiments the fluorescence may be dispersed and its spectrum detennined with a traditional spectrometer. In suitable cases this could be the emission from a single electronic-vibrational-rotational level of a molecule and the experimenter can study how the spectrum varies with level. 

If any atoms have nuclear spin this part of the total wave function can be factorized and the energy treated additively. ft is for these reasons that we can treat electronic, vibrational, rotational and NMR spectroscopy separately. 

It is important to realize that electronic spectroscopy provides the fifth method, for heteronuclear diatomic molecules, of obtaining the intemuclear distance in the ground electronic state. The other four arise through the techniques of rotational spectroscopy (microwave, millimetre wave or far-infrared, and Raman) and vibration-rotation spectroscopy (infrared and Raman). In homonuclear diatomics, only the Raman techniques may be used. However, if the molecule is short-lived, as is the case, for example, with CuH and C2, electronic spectroscopy, because of its high sensitivity, is often the only means of determining the ground state intemuclear distance. 

All by electron diffraction exceptamicrowave, vibrational-rotational spectroscopy. Standard deviations are 5 or less in the units of the last digit, except where given. 

The use of tunable lasers as sources in electronic absorption and emission spectroscopy has made possible a very considerable increase in resolution and precision. Electronic spectra are often difficult to analyze because of the many transitions involved. However, with a tunable laser source, one can tune the laser frequency to a specific absorption frequency of the molecule under study and thus populate a single excited electronic vibration-rotation energy level the resulting fluorescence emission spectrum is then simple, and easy to analyze. 

High speed emission spectroscopy has been used to study free radicals and positive, negative, and multiple ions produced in explosions and flames. Many excited states would exist for many different species from coal subjected to high energy. Complex spectra would result. The combination of electronic-vibration-rotation transitions observable in emission spectroscopy... 

The observational techniques used are spectroscopic in all cases. Electronic and vibration-rotation spectroscopy have been used for the simplest structures such as methylene and the halomethylenes the phase in which the carbene is examined does not seem to have much influence on the observed spectra (Bass and Mann, 1962). For more complicated carbenes, structural information has been largely gleaned from EPR spectroscopy using the matrix isolation technique, and this of necessity restricts studies to triplet states. 

Although Dispersed Fluorescence (DF) spectroscopy is probably better classified as a form of double resonance spectroscopy, DF is discussed here because it is a form of emission spectroscopy where all of the emission originates from a single, laser-populated, upper electronic-vibrational-rotational level, (e, v, J ). A DF spectrum typically contains two [R J" = J — 1), P(J" = J + 1)] or three [i ( J — 1), Q(J ), P J +1)] rotational transitions per electronic-vibrational e",v" level. Often there is a progression of vibrational bands, [ v, v" = n), (v, v" = n + 1),. .. (v, v" = n + to)] where v" = n is the lowest vibrational level (band farthest to the blue) and v" = n + m is the highest vibrational level observable (limited either by the detector response or Franck-Condon factors) in the DF spectrum (see Fig. 1.8 and Fig. 1.15). 

For virtually any diatomic molecule, it is possible to measure rotational constants for the ground vibrational state, i.e. B, and for several excited vibrational states by one of the usual techniques rotational or vibration-rotation spectroscopy, pure rotational Raman spectroscopy, or electronic spectroscopy. It is a simple matter to extrapolate to Be, and from Be to derive re. 

Far-infrared and mid-infrared spectroscopy usually provide the most detailed picture of the vibration-rotation energy levels in the ground electronic state. However, they are not always possible and other spectroscopic methods are also important. 

The treatment of electronic motion is treated in detail in Sections 2, 3, and 6 where molecular orbitals and configurations and their computer evaluation is covered. The vibration/rotation motion of molecules on BO surfaces is introduced above, but should be treated in more detail in a subsequent course in molecular spectroscopy. 

There exist a series of beautiful spectroscopy experiments that have been carried out over a number of years in the Lineberger (1), Brauman (2), and Beauchamp (3) laboratories in which electronically stable negative molecular ions prepared in excited vibrational-rotational states are observed to eject their extra electron. For the anions considered in those experiments, it is unlikely that the anion and neutral-molecule potential energy surfaces undergo crossings at geometries accessed by their vibrational motions in these experiments, so it is believed that the mechanism of electron ejection must involve vibration-rotation... 

Before returning to the non-BO rate expression, it is important to note that, in this spectroscopy case, the perturbation (i.e., the photon s vector potential) appears explicitly only in the p.i f matrix element because this external field is purely an electronic operator. In contrast, in the non-BO case, the perturbation involves a product of momentum operators, one acting on the electronic wavefimction and the second acting on the vibration/rotation wavefunction because the non-BO perturbation involves an explicit exchange of momentum between the electrons and the nuclei. As a result, one has matrix elements of the form (P/ t)Xf > in the non-BO case where one finds lXf > in the spectroscopy case. A primary difference is that derivatives of the vibration/rotation functions appear in the former case (in (P/(J.)x ) where only X appears in the latter. 

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