Vibrational spectroscopy symmetry selection rule

Beyond such electronic symmetry analysis, it is also possible to derive vibrational and rotational selection rules for electronic transitions that are El allowed. As was done in the vibrational spectroscopy case, it is conventional to expand i j (R) in a power series about the equilibrium geometry of the initial electronic state (since this geometry is more characteristic of the molecular structure prior to photon absorption) ... 

Both infrared (IR) and Raman spectroscopy have selection rules based on the symmetry of the molecule. Any molecular vibration that results in a change of dipole moment is infrared active. For a vibration to be Raman active, there must be a change of polarizability of the molecule as the transition occurs. It is thus possible to determine which modes will be IR active, Raman active, both, or neither from the symmetry of the molecule (see Chapter 3). In general, these two modes of spectroscopy are complementary specifically, if a molecule has a center of symmetry, no [R active vibration is also Raman active. 

Infrared Absorption is a single-photon process. Here, also, kiR = K 0 applies. Thus, infrared absorption detects only phonons at the F point of the first BZ. In this case, we have oo = L2, where ho) is the quantum energy of the infrared radiation. The frequencies or the wavenumbers of the optical phonons in molecular crystals are of the order of 3 THz or 100 cm" thus the wavelengths of infrared absorption are of the order of 100 /xm. Infrared spectroscopy of phonons in molecular crystals is therefore in fact far-infrared spectroscopy. The symmetry selection rules are complementary to those for Raman scattering for vibrations with u and g states w g transitions are allowed and g g transitions are forbidden. 

Vibronic-coupling theory has been a well established area of research since many years. The basic elements of the theory are the concept of dia-batic electronic states, the normal-mode description of vibrational motion, and the application of symmetry selection rules to derive appropriate model Hamiltonians. The applications of vibronic-coupling theory cover the full range of molecular spectroscopy, including, in particular, optical absorption and emission and photoelectron spectroscopy. Typical spectroscopic phenomena associated with vibronic interactions are the appearance of nominally forbidden electronic bands, the excitation of nontotally symmetric modes, or unusual and complex vibronic fine structures of electronic spectra. A fairly comprehensive and up-to-date exposition of vibronic-coupling theory is provided by the monograph of Bersuker and Polinger. ... 

This result is tremendously useful, it not only leads to selection rules for vibrational spectroscopy but also, as was the case with electronic wavefunctions (see 8-2), allows us to predict from inspection of the character table the degeneracies and symmetries which are allowed for the fundamental vibrational wavefunctions of any particular molecule. 

In this chapter, we discuss the various applications of group theory to chemical problems. These include the description of structure and bonding based on hybridization and molecular orbital theories, selection rules in infrared and Raman spectroscopy, and symmetry of molecular vibrations. As will be seen, even though most of the arguments used are qualitative in nature, meaningful results and conclusions can be obtained. 

The second problem relates to the inclusion, or otherwise, of molecular symmetry arguments. There is no avoiding the fact that an understanding of molecular symmetry presents a hurdle (although I think it is a low one) which must be surmounted if selection rules in vibrational and electronic spectroscopy of polyatomic molecules are to be understood. This book surmounts the hurdle in Chapter 4, which is devoted to molecular symmetry but which treats the subject in a non-mathematical way. For those lecturers and students who wish to leave out this chapter much of the subsequent material can be understood but, in some areas, in a less satisfying way. 

As stated in Section 1.7, selection rules are markedly different between IR and Raman spectroscopies. Thus, some vibrations are only Raman-active while others are only IR-active. Typical examples are found in molecules having a center of symmetry for which the mutual exclusion rule holds. In general, a vibration is IR-active, Raman-active, or active in both however, totally symmetric vibrations are always Raman-active. 

Chemical symmetry has been noted and investigated for centuries in crystallography which is at the border between chemistry and physics. It was more physics when crystal morphology and other properties of the crystal were described. It was more chemistry when the inner structure of the crystal and the interactions between its building units were considered. Later, descriptions of molecular vibrations and the establishment of selection rules and other basic principles happened in all kinds of spectroscopy. This led to another uniquely important place for the symmetry concept in chemistry with practical implications. 

The considerations on the symmetries of the ground and excited states and the above conditions lead to the selection rule for infrared spectroscopy A fundamental vibration will be infrared active if the corresponding normal mode belongs to the same irreducible representation as one or more of the Cartesian coordinates. 

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. 

Raman Selection Rules. For polyatomic molecules a number of Stokes Raman bands are observed, each corresponding to an allowed transition between two vibrational energy levels of the molecule. (An allowed transition is one for which the intensity is not uniquely zero owing to symmetry.) As in the case of infrared spectroscopy (see Exp. 38), only the fundamental transitions (corresponding to frequencies v, V2, v, ...) are usually intense enough to be observed, although weak overtone and combination Raman bands are sometimes detected. For molecules with appreciable symmetry, some fundamental transitions may be absent in the Raman and/or infrared spectra. The essential requirement is that the transition moment F (whose square determines the intensity) be nonzero i.e.. 

For energy relevant to vibrational spectroscopy, neutron-wavelengths are similar to chemical bonds or unit cell sizes. For example, Q can be as large as w 30 A-1 for an incident energy of 500 meV (ss 4000 cm-1). Therefore, the phase correlation of collective oscillations can be probed via momentum transfer. Symmetry related selection rules are no longer relevant. 

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. 

---