Inelastic selection rules

Perhaps the best known and most used optical spectroscopy which relies on the use of lasers is Raman spectroscopy. Because Raman spectroscopy is based on the inelastic scattering of photons, the signals are usually weak, and are often masked by fluorescence and/or Rayleigh scattering processes. The interest in usmg Raman for the vibrational characterization of surfaces arises from the fact that the teclmique can be used in situ under non-vacuum enviromnents, and also because it follows selection rules that complement those of IR spectroscopy. 

Cyvin, S. J., Rauch, J. E. and Decius, J. C. (1965) Theory of hyper-Raman effects (nonlinear inelastic light scattering) selection rules and depolarization ratios for the second-order polarizability. 

A further technique exists for the determination of triplet energy levels. This technique, called electron impact spectroscopy, involves the use of inelastic scattering of low-energy electrons by collision with molecules. The inelastic collisions of the electrons with the molecules result in transfer of the electron energy to the molecule and the consequent excitation of the latter. Unlike electronic excitation by photons, excitation by electron impact is subject to no spin selection rule. Thus transitions that are spin and/or orbitally forbidden for photon excitation are totally allowed for electron impact excitation. 

Section II will discuss the basic phenomena of inelastic tunneling from the viewpoint of the experimentalist. Section III will treat peak shapes, shifts, and widths. Section IV will deal with intensities and selection rules in IETS. Finally, Section V includes some recent applications of IETS to the fields of chemisorption and catalysis, and to the at first glance unrelated field of surface enhanced Raman spectroscopy. 

The cross-section in Eq. (1 illustrates another distinguishing feature of inelastic neutron scattering for vibrational spectroscopy, i.e., the absence of dipole and polarizability selection rules. In contrast, it is believed that in optical and inelastic electron surface spectroscopies that a vibrating molecule must possess a net component of a static or induced dipole moment perpendicular to a metal surface in order for the vibrational transition to be observed ( 7,8). This is because dipole moment changes of the vibrating molecule parallel to the surface are canceled by an equal image moment induced in the metal. 

Vibrations in molecules or in solid lattices are excited by the absorption of photons (infrared spectroscopy), or by the scattering of photons (Raman spectroscopy), electrons (electron energy loss spectroscopy EELS), or neutrons (inelastic neutron scattering). In case the vibration is excited by the interaction of the bond with a wave field - as with photons and electrons - the excitation is subject to strict selection rules. Collisions, on the other hand, excite all vibrational modes. 

Jeyes, S.R., McCaffery, A.J., Rowe, M.D. and Kato, H. (1977). Selection rules for collisional energy transfer in homonuclear diatomics. Rotationally inelastic collisions, Chem. Phys. Lett., 48, 91-94. 

Another class of techniques monitors surface vibration frequencies. High-resolution electron energy loss spectroscopy (HREELS) measures the inelastic scattering of low energy ( 5eV) electrons from surfaces. It is sensitive to the vibrational excitation of adsorbed atoms and molecules as well as surface phonons. This is particularly useful for chemisorption systems, allowing the identification of surface species. Application of normal mode analysis and selection rules can determine the point symmetry of the adsorption sites./24/ Infrarred reflectance-adsorption spectroscopy (IRRAS) is also used to study surface systems, although it is not intrinsically surface sensitive. IRRAS is less sensitive than HREELS but has much higher resolution. 

Fig. 2.2-Ic illustrates a similar process, the inelastic scattering of neutrons. Irradiating molecules with mono-energetic neutrons produce scattered neutrons according to an energy balance equivalent to Eq. 2.2-1. While Raman scattering as well as infrared absorption of symmetric molecules obeys strict selection rules, which allow or forbid the activity of certain vibrations in these spectra, inelastic scattering of neutrons is not subject to such rules. It is not usually applied in analytical chemistry, but it is used to study lattice vibrations of crystals in solid-state physics and dynamics of liquids.

Information regarding the normal modes of a polyatomic molecule, which are not IR active, may often be obtained from the Raman spectrum. Raman spectroscopy is an inelastic-scattering technique rather than requiring the absorption or emission of radiation of a particular energy. The selection rule differs from the IR in that it is required that the incident electric field of the radiation can induce a changing dipole moment of the molecule. This results in a different symmetry requirement for the normal modes of vibration to be Raman active, since it now depends on the polarizability of the molecule. 

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