Energy dependence vibrational excitation intensity

Excitation Eunctions of O2 and 02-Doped Ar Eilms. Resonances can be best identified by the structures they produce in excitation functions of a particular energy-loss process (i.e., the incident-electron energy dependence of the loss). Fig. 7 is reproduced from a recent study [118] of the electron-induced vibrational and electronic excitation of multilayer films of O2 condensed on the Pt(lll) surface and shows the incident electron energy dependence of major losses at the indicated film thickness and scattering angles. Also shown in this figure is the scattered electron intensity of the inelastic background... 

Figure 2.1 Schematic representation of the ground and electronic excited potential energy surfaces (PESs) and the corresponding absorption spectra of the parent molecule, resulting from the reflection of different initial wavefunctions on a directly dissociative PES (a) absorption from a vibrationless ground state consists of a broad continuum and (b) absorption from a vibrationally excited state shows that extended regions are accessed, leading to a structured spectrum with intensities of the features being dependent on the Franck-Condon factors. Reproduced with permission from Ref. [34]. Reproduced by permission of lOP Publishing.

The position of the 0 O band defines the energy of the excited state relative to that of the ground state, E0 0 = hv0 0. It can usually be located accurately in gas-phase spectra, especially in high-resolution spectra that can be obtained in low-temperature molecular beams. In solution, however, many molecules do not exhibit any vibrational fine structure in their electronic absorption spectra, so that it is difficult to determine v0 0. Moreover, the intensity dependence illustrated in Figure 2.10 holds only for symmetry-allowed transitions (see Section 4.4). That symmetry-forbidden transitions are observable at all as weak absorptions is due to vibrational borrowing vibronic transitions to upper (non-totally symmetric) vibrational levels become weakly allowed when the total symmetry of the vibronic transition is considered. Forbidden 0 0 bands are sometimes (barely) detectable in solution spectra due to symmetry perturbations induced by the solvent, but possible contributions from hot bands (Section 2.1.4) must be taken into account. 

One point to mention is that SFG is not fully independent of the gaseous environment. At pressures above 1 Torr, a significant energy-dependent infrared absorption occurs via vibrational and rotational excitation of gas phase molecules. Since the intensity of the SFG depends on the input infrared beam intensity, gas pressure indirectly influences the outcome of SFG. To compensate for such an effect, several strategies have been proposed. Another point is that the SFG phenomenon depends on both infrared and Raman absorption coefficients and therefore correlation of band intensity with adsorbate concentration is not straightforward. 

The natural frequency of tubes depends primarily on their geometry and material of construction. The intensity of vibration is evidenced by the amount of periodic movement the extent of this peak-to-peak movement about the at-rest centerline is termed the amplitude of vibration. Energy must be available to excite the tubes into vibration. The energy of vibration is dissipated by internal and external damping. The exciting force could be the result of ... 

---