Raman scattering pure rotational

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

High-resolution Raman spectroscopy of gases with different He-Ne and Ar laser lines was also performed by Weber etal. The authors determined relative scattering cross-sections for the pure rotational Raman spectrum of Oj. 

In a similar fashion, pure rotational Raman scattering can... 

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.

Figure 6.1-27 The pure rotational photoacoustic Raman (PARS) spectrum of CO2 gas at a pressure of 80 kPa (600 Torr) pump laser wavelength at 532 nm. Note the complete absence of any acoustical signal due to Rayleigh scattering (at 532 nm) (Barrett, 1981).

A special remark should be made concerning the transitions without changes of the energy of the internal degrees of freedom, i.e., about pure rotational Raman scattering. In the case of an even number of electrons, such transitions are possible if in the expansion of the even (odd) (with respect to time reversal) tensor operator C 71 there are representations contained in the symmetric [P] (antisymmetric P ) quadrate of the representation T. In the case of an odd number of electrons, at least one of the representations T in the expansion of the even (odd) operator C 71 (with respect to time reversal) is contained in P ([P]). 

Let us use these selection rules for investigating the main features of the Rayleigh and pure rotational Raman scattering by spherical-top molecules in the lowest vibronic states (Ogurtsov et al., 1978). The polarizability tensors dif2i and can be expanded into components of irreducible tensor operators that in cubic groups transform as E, T2, and T, respectively. Here the behavior of the operators dir 71 with respect to time reversal 0 has to be taken into consideration. To do this, we use the explicit form of the operator djj(a>) in Cartesian coordinates ... 

In the case of degenerate E states we have [E2] = A + E and E2 = A2, and therefore here the pure rotational Raman spectra of quadrupole type are possible. In the case of T terms also, pseudovector scattering is allowed, since in this case T2 contains T. Finally, analogously one can make sure that in the states E n and E5/2 pure rotational scattering of pseudovector type only is possible, while in the states G3 2 both quadrupole and pseudo vector scattering should take place. 

Note that transitions with T = F should also be related to a pure rotational one. However, in the case of strong vibronic coupling there may be another low-lying vibronic state with a symmetry different from that of the ground state. Therefore in these cases the pure rotational Raman spectrum can be superposed by the spectrum of vibronic-rota-tional scattering. 

It follows from these equations that in the case under consideration the pure rotational Raman spectrum consists of lines corresponding to three types of O, P, Q, R, and S transitions EJ — 72(0, P, Q, R, S), EJ A,72(0, P, Q, R, S ), and A7, - 72(0", P", Q", R", S"). The lines denoted by one and two primes are displaced with respect to the nonprimed ones by 2A and -2A, respectively. Note that the scalar scattering gives lines of the type Q only with cross section, as follows ... 

Raman optical activity has only been measured so far in pure liquids and strong solutions. Crystals and powders are harder to study crystals must be polished and oriented carefully to eliminate artefacts, whereas multiple scattering in powders depolarizes the incident light. It would be of great interest to measure pure rotational, and rotational-vibrational, ROA in gases, but insufficient scattered intensity has so far prevented this. An additional complication in resonance scattering is that circular dichroism of the incident beam can contribute to the measured circular intensity difference. 

Pure rotational transitions of symmetrical diatomic molecules like dihydrogen are forbidden in infrared spectroscopy by the dipole selection rule but are active in Raman spectroscopy because they are anisotropically polarisable. They are in principle observable in INS although the scattering is weak except for dihydrogen. These rotational transitions offer the prospect of probing the local environment of the dihydrogen molecule, as we shall see in this chapter. 

In this book we are concerned only with that part of the spectrum dependent on pure rotations and translations of molecules. No further discussion of the vibrational Raman scattering is given. Thus Eq. (3.3.3) is used, but always with the rigid-frame polarizabilities. We refer to this type of scattering as Rayleigh-Brillouin" scattering.11... 

What are the consequences of these considerations for depolarized light scattering In a dilute gas where reorientation is predominantly inertial, we expect the spectrum to be what is normally called the pure rotational Raman spectrum of the molecule. As higher densities are approached, the discrete spectral lines broaden and overlap to form a continuous band. We show how the band shape can be computed for freely rotating linear molecules and spherical top molecules and then indicate the assumptions that have been used by several authors to include collisions in the theory. 

Since the coefficients (dp/dq)o are very small, one needs large incident intensities to observe hyper-Raman scattering. Similar to second-harmonic generation (Vol. 1, Sect. 5.8), hyper-Rayleigh scattering is forbidden for molecules with a center of inversion. The hyper-Raman effect obeys selection rules that differ from those of the linear Raman effect. It is therefore very attractive to molecular spectroscopists since molecular vibrations can be observed in the hyper-Raman spectrum that are forbidden for infrared as well as for linear Raman transitions. For example, spherical molecules such as CH4 have no pure rotational Raman spectrum but a hyper-Raman spectrum, which was found by Maker [357]. A general theory for rotational and rotational-vibrational hyper-Raman scattering has been worked out by Altmann and Strey [358]. 

If the initial and final energy states involved in a Raman transition belong to the rotational level manifold of two different vibrational states, then slightly different conditions than those for pure rotational Raman scattering are encountered in observing the related spectra. 

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