Vibrational transitions Raman

Figure 6.7 Rotational transitions accompanying a vibrational transition in (a) an infrared spectrum and (b) a Raman spectrum of a diatomic molecule...

The rotational selection rule for vibration-rotation Raman transitions in diatomic molecules is... 

As for a diatomic molecule, the general harmonic oscillator selection mle for infrared and Raman vibrational transitions is... 

In the most usual cases, where the lower level is the zero-point level, F(i/ ") = A and the requirement for a Raman vibrational transition becomes... 

Raman scattering is normally of such very low intensity that gas phase Raman spectroscopy is one of the more difficult techniques. This is particularly the case for vibration-rotation Raman spectroscopy since scattering involving vibrational transitions is much weaker than that involving rotational transitions, which were described in Sections 5.3.3 and 5.3.5. For this reason we shall consider here only the more easily studied infrared vibration-rotation spectroscopy which must also be investigated in the gas phase (or in a supersonic jet, see Section 9.3.8). 

For a molecule belonging to the D2h point group deduce whether the following vibrational transitions, all from the zero-point level, are allowed in the infrared spectmm and/or Raman spectmm, stating the direction of the transition moment and/or the component of the polarizability involved ... 

Although it is less often done, I have used an analogous symbolism for pure vibrational transitions for the sake of consistency. Here N refers to a vibrational (infrared or Raman) transition from a lower state with vibrational quantum number v" to an upper state v in the vibration numbered N. 

Resonance Raman (RR) spectroscopy provides information about the vibrational characteristics of a chromophore, for example, a metal center, within the complex environment of a protein. In RR spectra, those vibrational transitions are observed selectively that are coupled to electronic transitions. In iron sulfur proteins, this technique has been used to resolve the complex electronic absorption spectra and to identify both vibrational and electronic transitions. 

In either case, the information on the vibrational transition is contained in the energy difference between the excitation radiation and the inelastically scattered Raman photons. Consequently, the parameters of interest are the intensities of the lines and their position relative to the Rayleigh line, usually expressed in wavenumbers (cm 1). As the actually recorded emissions all are in the spectral range determined by the excitation radiation, Raman spectroscopy facilitates the acquisition of vibrational spectra through standard VIS and/or NIR spectroscopy. 

In general, though, Raman spectroscopy is concerned with vibrational transitions (in a manner akin to infrared spectroscopy), since shifts of these Raman bands can be related to molecular structure and geometry. Because the energies of Raman frequency shifts are associated with transitions between different rotational and vibrational quantum states, Raman frequencies are equivalent to infrared frequencies within the molecule causing the scattering. 

Information concerning conformation, tacticity and crystallinity may also be obtained (1). Vibrational transitions accesssible to IR spectroscopy are governed by the selection rule that there must be a change in dipole moment during excitation of the polymer vibrations. Thus symmetric vibrations which are detected by Raman spectroscopy are inaccessible to IR absorption measurements. 

Resonance-enhanced Raman scattering occurs when the energy of the Incident radiation, hvg. Is close to or within an electronic absorption band of the sample (7,8). In this case, vlbronlc coupling with the electronically excited state Increases the probability of observing Raman scattering (hv-gg) from vibrational transitions In the electronic ground state (Figure lb). The Intensity of such resonance-enhanced vibrational transitions can be described In simplified terms as ... 

The other form of optical activity in vibrational transitions is known as Raman optical activity (ROA). Here, also, one measures an intensity difference for left compared to right circularly polarized incident radiation however, optical activity in light scattering has no direct analog in electronic spectroscopy. ROA was first measured by Laurence Barron, A. D. Buckingham, and M. P. Bogaard in 1973 (9) and several reviews of the subject have since appeared (10-14). 

The polarizability tensor of a molecule related the components of the induced dipole moment of the molecule to the components of the electric field doing the inducing. It therefore has 9 components, axx, ctxy, etc., only 6 of which are independent. The theory of the Raman effect shows that a vibrational transition, from the totally symmetric ground state to an excited state of symmetry species F, will he Raman active if at least one of the following direct products contains the totally symmetric representation ... 

For simplicity of analysis, we consider just a single vibrational transition, which is characterized by the Raman cross section,... 

The rule of mutual exclusion states that for a molecule with a center of symmetry, a given vibrational transition cannot appear in both the IR and Raman spectra. (For the proof, see Chapter 9.) Some fundamentals may be both IR and Raman inactive their frequencies can often be determined from IR or Raman combination bands. 

The selection rules for Raman vibrational transitions are also readily derived from group theory. Here, the transition probability depends on integrals involving the components of the molecular polarizability matrix a. Since a is symmetric, it has only six independent components axx aw axi axr ayi aMf These six quantities can be shown14 to transform the same way the six functions... 

For example, Raman spectroscopy techniques show vibrational transitions that can be attributed to the HNO3 molecule as well as to the NOJ ion.11 By using the intensities of the Raman bands to measure the concentrations of the species in solution, an equilibrium constant can be written... 

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