Rotational absorption, pure Raman

Pure rotational and vibrational Raman spectra of At2 Raman spectroscopic study of kinetics of Ar, formation in a supersonic expansion seeded with Nj Electronic absorption spectrum of HgAr Rotational Zeeman effect in ArHBr t HgCl2 collision complex formed in harpoon reaction of Hg with Clj investigated via excitation of the HgCL van der Waals complex... 

As in the case of absorption and fluorescence emission spectroscopy, selection rules apply for the Raman transitions between rotational energy levels. However, since two photons are involved in the process, each of angular momentum Lphoton = 1. angular momentum conservation requires that the difference between the initial and final rotational levels must be two. As the selection rule for pure Raman spectra, one finds... 

A translational line like the one seen above in rare gas mixtures is relatively weak but discernible in pure hydrogen at low frequencies (<230 cm-1), Fig. 3.10. However, if a(v)/[l —exp (—hcv/kT)] is plotted instead of a(v), the line at zero frequency is prominent, Fig. 3.11 the 6o(l) line that corresponds to an orientational transition of ortho-H2. Other absorption lines are prominent, Fig. 3.10. Especially at low temperatures, strong but diffuse So(0) and So(l) lines appear near the rotational transition frequencies at 354 and 587 cm-1, respectively. These rotational transitions of H2 are, of course, well known from Raman studies and correspond to J = 0 -> 2 and J = 1 — 3 transitions J designates the rotational quantum number. These transitions are infrared inactive in the isolated molecule. At higher temperatures, rotational lines So(J) with J > 1 are also discernible these may be seen more clearly in mixtures of hydrogen with the heavier rare gases, see for example Fig. 3.14 below. 

The electronic spectrum of F2, in absorption and in emission, has been photographed with sufScient resolution to warrant rotational analysis of many bands the dissociation energy, Do(F2), was estimated to be 12 920 50cm . New measurements of the pure rotational Raman spectrum of F2 have been reported by Long et al., who have calculated more precise values of the rotational constants Bo and Do and of the bond lengths to and r . 

Before discussing vibration-rotation band shapes, it is appropriate to consider "pure rotational" Raman spectra in dense fluids (often called inelastic light scattering). The argument closely parallels that for i.r. absorption, but with the added complication of polarized and depolarized scattering. In the depolarized case, one has a "self" term which is ... 

We now need to take up the vibrational contributions to the absorption and the Raman correlation functions. Ordinarily, the motion associated with a normal mode is not appreciably coupled either with the orientation of the molecule, or with other normal modes in the same molecule or in other molecules. (Treatments of this coupling do exist, but are too advanced for present purposes.) When these assumptions are made, the spectral time-correlation functions simplify greatly. For example, for the infrared case, the pure rotational part is augmented by a series of terms, one for each normal mode. We can consider these separately since, as mentioned above, they usually correspond to vibration-rotation bands which in favorable cases are isolated spectral features that can be Fourier transformed or otherwise analyzed independently from the other bands. The time-correlation function for the infrared absorption associated with the Vth normal mode is thus written as... 

The selection rules for pure rotational transitions of symmetric tops are A7 = 1, AAi = 0 for direct absorption or emission, and A/= 1 or 2, AAi = 0 for the Raman effect. We obtain simple spectra in both cases, with a single series of lines (A/= +1) in absorption and two series (A7 = +1 and +2) in the Raman effect. Neglecting centrifugal distortion, these series have constant spacings of 2B or AB, and lines for all values of K coincide. If there is centrifugal distortion, separate lines can be observed for the different K values that are possible for each value of J, with frequencies (for A7 = 1) given by... 

The pure rotation spectrum of an asymmetric top is very complex, and cannot be reduced to a formula giving line positions. Instead, it has to be dealt with by calculation of the appropriate upper and lower state energies (Section 7.2.2). The basic selection rule, A7 = 0, 1, applies to absorption/emission spectra, and there are other selection rules. These depend on the symmetry of the inertial ellipsoid, which is always Dan, but the orientations of the dipole moment components depend on the symmetry of the molecule itself. For the rotational Raman effect A7= 2 transitions are allowed as well. The selection rules for pure rotational spectra are described in more detail in the on-line supplement for Chapter 7. 

For a symmetric top, only B can be determined easily from a pure rotation spectrum or a vibration- -otation band in absorption, and the same problem can arise. This is described in more detail in the on-line supplement for Chapter 7. It is also possible in principle to determine A for a symmetric top if the Raman spectrum is studied with sufficient resolution, but this has been done only for a few simple molecules. In other cases, A has been found from high-resolution IR spectra by making use of a breakdown of the simple rotational selection mles arising from perturbations, or couplings between close-lying levels. However, these occur only by chance in particular systems. 

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