Rotational transitions Raman

Plenary 9. J W Nibler et al, e-mail address niblerj chem.orst.edu (CARS and SRS). High resolution studies of high lymg vibration-rotational transitions in molecules excited in electrical discharges and low density monomers and clusters in free jet expansions. Ionization detected (REMPI) SRS or IDSRS. Detect Raman... 

Electronic, vibrational and rotational transitions may be involved in Raman scattering but, in this chapter, we consider only rotational transitions. 

The mechanism for Stokes and anti-Stokes vibrational Raman transitions is analogous to that for rotational transitions, illustrated in Figure 5.16. As shown in Figure 6.3, intense monochromatic radiation may take the molecule from the u = 0 state to a virtual state Vq. Then it may return to u = 0 in a Rayleigh scattering process or to u = 1 in a Stokes Raman transition. Alternatively, it may go from the v = state to the virtual state Fj and return to V = (Rayleigh) or to u = 0 (Raman anti-Stokes). Flowever, in many molecules at normal... 

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

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). 

The wave mixing is much more efficient when (vj — V2) = v, where is the wavenumber of a Raman-active vibrational or rotational transition of the sample. 

Additional experimental verification that molecules of hydrogen in condensed phases are in states approximating those for free molecules is provided by the Raman effect measurements of McLennan and McLeod.13 A comparison of the Raman frequencies found by them and the frequencies corresponding to the rotational transitions / = 0—>/ = 2 and/= 1— / = 3 (Table II) shows that the intermolecular interaction in liquid hydrogen produces only a very small change in these rotational energy levels. 

Trace (a) of Fig. 28 represents part of the pure rotational laser Raman spectrum of 02. This example is a single scan of the S3 transition J = 3 to J — 5 in the ground state. This transition is split into three components... 

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. 

For any vibrational mode, the relative intensities of Stokes and anti-Stokes scattering depend only on the temperature. Measurement of this ratio can be used for temperature measurement, although this application is not commonly encountered in pharmaceutical or biomedical applications. Raman scattering based on rotational transitions in the gas phase and low energy (near-infrared) electronic transitions in condensed phases can also be observed. These forms of Raman scattering are sometimes used by physical chemists. However, as a practical matter, to most scientists, Raman spectroscopy means and will continue to mean vibrational Raman spectroscopy. 

CC is the other dominant product of hydrocarbon-fueled combustion and its CARS flame spectrum (23)is displayed in Figure 1A. The spectrum is complicated by Fermi resonance and the fact that the rotational transitions are closely overlapped. This precludes treating them as independently broadened and so-called collisional narrowing may need to be taken into account. Computer modelling is currently in progress. Since all hydrocarbon fuels are Raman-active,CARS should ultimately be capable of monitoring total hydrocarbon concentrations during combustion as well. 

Although Raman spectra are normally observed for vibrational and rotational transitions, it is possible to observe Raman spectra of electronic transitions between ground states and low-energy excited states. 

Periodic oscillations in this dipole can act as a source term in the generation of new optical frequencies. Here a is the linear polarizability discussed in Exps. 29 and 35 on dipole moments and Raman spectra, while fi and x are the second- and third-order dielectric susceptibilities, respectively. The quantity fi is also called the hyperpolarizability and is the material property responsible for second-harmonic generation. Note that, since E cos cot, the S term can be expressed as -j(l + cos 2 wt). The next higher nonlinear term x is especially important in generating sum and difference frequencies when more than one laser frequency is incident on the sample. In the case of coherent anti-Stokes Raman scattering (CARS), X gives useful information about vibrational and rotational transitions in molecules. 

Because of the high monochromaticity of the incident laser beam, transitions differing by even a fraction of a wavenumber from the Rayleigh frequency can be detected, which makes pure rotational transitions accessible to laser-Raman spectroscopy. 

The very different spectra of iodine obtained under continuum and discrete resonance-Raman conditions are illustrated in Fig. 11 for resonance with the B state, whose dissociation limit is 20,162 cm . In the case illustrated of discrete resonance-Raman scattering, Xl =514.5 nm, and specific re-emission results from an initial transition from the v" = 1 vibrational, J" = 99 rotational level of the X state to the v = 58, J = 100 level of the B state, i.e. the transition is 58 - l" R(99). Owing to the rotational selection rule for dipole radiation, AJ = 1, a pattern of doublets appears in the emission. Clearly, the continuum resonance-Raman spectrum of iodine (Xl = 488.0 nm) is very different from the discrete case spectrum. The structure, which arises from the 0,Q, and S branches of the multitude of vibration-rotation transitions occurring, can be analysed in terms of a Fortrat diagram, as done for gaseous bromine (67). 

B. Continuum resonance-Raman scattering fromj2 gas with excitation at 488.0 nm which is above the dissociation limit of the B( ITou) <- X( Sg) transition. The fine structure of each vibrational overtone is attributable to the Q, O and S branches of the multitude of rotational transitions occurring... 

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. 

The essential features of CARS can be summarized as follows. A typical CARS set-up involves the use of a pump laser beam at frequency cOi and a red-shifted laser beam at frequency cOg (Stokes beam). These beams are crossed within the Raman medium and, when their frequency difference equals a vibration-rotation or a purely rotational transition in the molecule, a third external laser beam at frequency (O2 can probe (in a fashion... 

The Raman cross-section da/dQ. is a function of the properties of the vibration-rotation transitions being summed. 

Vibrational spectra are accompanied by rotational transitions. Rgure 1-4 shows the rotational fine structure observed for the gaseous ammonia molecule. In most polyatomic molecules, however, such a rotational fine structure is not observed because the rotational levels are closely spaced as a result of relatively large moments of inertia. Vibrational spectra obtained in solution do not exhibit rotational fine structure, since molecular collisions occur before a rotation is completed and the levels of the individual molecules are perturbed differently. Since Raman spectra are often obtained in liquid state, they do not exhibit rotational fine structure. 

Gas phase Raman measurements can, of course, resolve individual rotational transitions, so it is necessary to consider rotational-vibrational electronic states in the general transition polarizability (2.18). The classical isotropic averages derived in the previous section provide a useful background because, in accordance with van Vleck s principle of spectroscopic stability [14, a quantum-statistical average over all allowed transitions should yield the... 

Natural ROA offers the interesting prospect of measuring optical activity in pure rotational transitions of gas phase chiral molecules. Although such observations have not yet been reported, the detailed theory of rotational ROA in chiral symmetric tops has been published lS7, and the experiment should be feasible using existing technology such as optical multichannel detection. It is also possible that one of the coherent Raman techniques discussed below could be advantageous. 

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