Vibrational excitation symmetric molecules

Reaction (68) is important in the operation of the C02-N2 laser [88], in which vibrationally excited nitrogen molecules collide with ground state C02 to produce excitation by the inverse process. The (001) level subsequently decays by stimulated emission of 10.6-micron radiation to the symmetric stretch (100) level (see Figure 3.8). 

Treating vibrational excitations in lattice systems of adsorbed molecules in terms of bound harmonic oscillators (as presented in Chapter III and also in Appendix 1) provides only a general notion of basic spectroscopic characteristics of an adsorbate, viz. spectral line frequencies and integral intensities. This approach, however, fails to account for line shapes and manipulates spectral lines as shapeless infinitely narrow and infinitely high images described by the Dirac -functions. In simplest cases, the shape of symmetric spectral lines can be characterized by their maximum positions and full width at half maximum (FWHM). These parameters are very sensitive to various perturbations and changes in temperature and can therefore provide additional evidence on the state of an adsorbate and its binding to a surface. 

Figure 2.7 Vibrational excitation spectra in the region of the fundamental N-H and C-H symmetric stretches of pyrrole (a) photoacoustic Raman spectrum in a static cell at a pressure of 6.5 Torr and (b) H action spectrum obtained by 243.135 nm dissociation of jet-cooled molecules at a delay of 10 ns between the SRS and UV beams. The intensity scale of each panel is different. Reproduced with permission from Ref. [87]. Copyright (2011) AlP Publishing LLC.

In addition to the processes just discussed that yield vibrationally and rotationally excited diatomic ions in the ground electronic state, vibrational and rotational excitations also accompany direct electronic excitation (see Section II.B.2.a) of diatomic ions as well as charge-transfer excitation of these species (see Section IV.A.l). Furthermore, direct vibrational excitation of ions and molecules can take place via charge transfer in symmetric ion molecule collisions, as the translational-to-internal-energy conversion is a sensitive function of energy defects and vibrational overlaps of the individual reactant systems.312-314... 

We now consider hydrogen transfer reactions between the excited impurity molecules and the neighboring host molecules in crystals. Prass et al. [1988, 1989] and Steidl et al. [1988] studied the abstraction of an hydrogen atom from fluorene by an impurity acridine molecule in its lowest triplet state. The fluorene molecule is oriented in a favorable position for the transfer (Figure 6.18). The radical pair thus formed is deactivated by the reverse transition. H atom abstraction by acridine molecules competes with the radiative deactivation (phosphorescence) of the 3T state, and the temperature dependence of transfer rate constant is inferred from the kinetic measurements in the range 33-143 K. Below 72 K, k(T) is described by Eq. (2.30) with n = 1, while at T>70K the Arrhenius law holds with the apparent activation energy of 0.33 kcal/mol (120 cm-1). The value of a corresponds to the thermal excitation of the symmetric vibration that is observed in the Raman spectrum of the host crystal. The shift in its frequency after deuteration shows that this is a libration i.e., the tunneling is enhanced by hindered molecular rotation in crystal. 

The main purpose of this chapter is to emphasize the intimate relation between the topology of the dissociative PES and the vibrational excitation of the fragment molecule. In Sections 9.1 and 9.2 we consider exclusively direct processes. The photodissociation of symmetric molecules with two equivalent product channels is the topic of Section 9.3. Finally, vibrational state distributions following the decay of a long-lived intermediate complex will be discussed in Section 9.4. The theory... 

The electron-vibration coupling V has the same symmetry of the vibration. This is because the Hamiltonian is totally symmetric under transformations of the point group of the ensemble molecule plus substrate. In Appendix we give further details in particular Eq. (A4) shows that in order to preserve the invariance of the Hamiltonian under transformation of the nuclear coordinates, the electronic coordinates must transform in the same way [37]. Hence, if a symmetric mode is excited, the electron-vibration coupling will also be symmetric in the electronic-coordinate transformations. Thus only electronic states of the same symmetry will give non-zero matrix elements for a symmetric vibration. This kind of reasoning can be used over the different vibrations of the molecule. 

The EMAP method has been used to compute elastic scattering and symmetric-stretch vibrational excitation cross sections for electron scattering by C02 [235], This is one of the first ab initio calculations of vibrational excitation for a polyatomic molecule. The results are in good agreement with experiment, which shows unusually large low-energy cross sections. The theory identifies a near-threshold... 

The Raman spectra are quicker and easier to determine than the infrared absorption spectra because ordinary optical equipment can be used, but frequently they are more difficult to interpret. The quantum restrictions in the two phenomena, particularly for symmetrical molecules, are not always the same, because the Raman spectrum involves an intermediate excited state of the molecule. For this reason, it is desirable to have the data of both Raman and infrared absorption spectra in order to determine completely the rotational and rotational-vibrational energy levels in the molecule. The Raman spectrum can be obtained in some solutions where direct absorption measurements are impossible because the solvent is opaque in the infrared. Aqueous solutions offer a good example of such a case. 

The result of summations in Eqn. (50) is largely determined by the spectrum of the intramolecular subsystem final state. The spectrum can be either discrete or continuous. For instance, in the case of H-atom abstraction from the molecule by the methyl radical the value of the thermal effect of the reaction is such that the energy evolved may be sufficient only to excite the fourth vibration level of the C-H bond of the CH4 molecule. In such small molecules the quasi-continuum region lies much higher [157]. For the symmetric reaction of radical pair transformation in dimethylglyoxime the thermal effect is nought, and the discreteness of the final intramolecular spectrum, in this case, is evident. If, however, as a result of the reaction, highly excited multiatom molecules are formed or dissociation of the excited molecules occurs, the intramolecular subsystem final state spectrum is continuous. 

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