Raman rotational-vibrational line

Figure 1. Rotational—vibrational line strength correction factors for pure rotational Raman scattering (fM)0 and for O-, S-, and Q-branch vibrational Raman scattering (foh fots, and folQ). The value J is the rotational quantum number of the initial level (O), Stokes (A), anti-Stokes.

In many cases, the infrared and Raman rotation-vibration spectra contribute complementary structure data, particularly for highly symmetric molecules. Due to the significantly different selection rules a greater line density is observed for Raman due to a larger selection of allowed changes in the rotational energy compared to infrared gas spectra. Raman spectroscopy is, on these grounds, also a valuable supplement to infrared studies. 

R branch, 364, 365 Radiation, by accelerated charge, 6 by electric quadrupolc, 39 by magnetic dipole, 39 by oscillating dipole, 43 Raman activity (see Scilection rules) Raman band types,, 366 Raman lines (see Raman spectrum) Raman rotation-vibration spectra, 365 Raman scattering, 48, 49 (See also Raman spoctnim)... 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

In the gaseous state coupling of the vibrational transitions with the rotational degrees of freedom give rise to rotational-vibrational bands (Fig. 2.6-1 A). The structures of these bands characterize the shape of a molecule and its symmetry (see Sec. 2.7). Spectral lines in the far-infrared range and in low-frequency Raman spectra are due to pure, quantized rotations of the molecules. Infrared and Raman spectra of gases are discussed in detail in Secs. 4.3.1 and 4.3.2. 

As soon as water-cooled low pressure mercury arcs had been developed in Toronto (Welsh et al., 1952), the resulting low linewidths of the exciting lines facilitated the resolution of rotational structure in the spectra. In a long series of investigations Stoicheff (1959) and Weber (1973) and their collaborators recorded photographically the pure rotational Raman spectra of a great number of molecules under high resolution, while Welsh and coworkers in Toronto (Stansbury et al.,1953 Welsh et ah, 1955 Feldman et ah, 1955 and 1956 Romanko et ah, 1955 Mathai et ah, 1956 Welsh, 1956 Allin et ah, 1967 Fast et ah, 1969) studied rotation-vibrational Raman bands. 

Since the occurrence of the Raman effect depends on the change in polarizability as vibration occurs, the selection rules are different for the Raman effect than they are for the infrared spectrum. In particular, in molecules with a center of symmetry the totally symmetric vibration is Raman-active, but is forbidden in the infrared since it produces no change in dipole moment. Thus the homonuclear diatomic molecules, H2, O2, N2, show the Raman effect but do not absorb in the infrared. There is also a purely rotational Raman eff ect in these molecules. However, in this case the selection rule is A J = 2. Thus we have for the rotational Stokes lines... 

However, in molecular crystals (see Sec. II.E), in addition to the lattice vibrations, one can observe rotational vibrations of the molecules about their principal axes of inertia these are the so-called librations (from libre in French, meaning free to rotate). Of course, the symmetry of the elementary cell of the crystal determines which vibrations and/or librations are manifested in the Raman spectra (see Sec. V.E). In the crystalline state, the interactions between atoms, ions or molecules are stronger, so that the observed lines are generally broader. Rotations of bonds such as —C—N or —O— H in nonmolecular crystals are also considered as librations. Likewise, any chemical radical free to rotate about its inertia axis can be said to librate (e.g., —CO3 or —SO4, as long as such motion is not blocked by additional bonds). 

The out-of-plane vibrations of thiazole correspond to C-type vibration-rotation bands and the in-plane vibrations to A, B, or (A + B) hybrid-type bands (Fig, 1-9). The Raman diffusion lines of weak intensity were assigned to A"-type oscillations and the more intense and polarized lines to A vibration modes (Fig. I-IO and Table 1-23). 

Suites 1 to VIII contain infrared frequencies corresponding to vibration-rotation bands of A, B, or (A-l-B) hybrid types and can thus be assigned to vibrations of A symmetry the corresponding Raman lines are generally polarized. 

The frequencies classified in suites IX and X belong to depolarized Raman lines and correspond to vibrations-rotation bands of the C type. They can be assigned to oscillations of A" symmetry. 

Fig. 3.8. The Q-branch Raman width alteration with condensation of nitrogen. The theoretical results for the strong (A) and weak (B) collision limits are shown together with experimental data for gaseous [89] ( ) and liquid nitrogen [145] ( ) (point a is taken from the CARS experiment of [136]). The broken curves in the inset are A and B limits whereas the intermediate solid curve presents the rotational contribution to line width at y = 0.3. The straight line estimates the contribution of vibrational dephasing [143], and the circles around it are the same liquid data but without rotational contribution.

The half-width (at half-height) and the shift of any vibrational-rotational line in the resolved spectrum is determined by the real and imaginary parts of the related diagonal element TFor linear molecules the blocks of the impact operator at k = 0,2 correspond to Raman scattering and that at k = 1 to IR absorption. The off-diagonal elements in each block T K, perform interference between correspond-... 

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