Raman effect, transitions

Figure 9.21 Transitions in the stimulated Raman effect in benzene...

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. 

Figure 2.52 Schematic representation of the transitions giving rise to the Raman effect. GS = ground electronic state, ES = excited electronic state, VS = virtual electronic stale, R = Rayleigh scattering, S = transitions giving rise to Stokes lines, AS = transitions giving rise to Anti-Stokes lines, RRS = transitions giving rise to resonance Raman.

The Raman effect arises when a photon is incident on a molecule and interacts with the electric dipole of the molecule. In classical terms, the interaction can be viewed as a perturbation of the molecule s electric field. In quantum mechanics the scattering is described as an excitation to a virtual state lower in energy than a real electronic transition with nearly coincident de-excitation and a change in vibrational energy. The scattering event occurs in 10 14 seconds or less. The virtual state description of scattering is shown in Figure 1. 

Raman spectroscopy is primarily useful as a diagnostic, inasmuch as the vibrational Raman spectrum is directly related to molecular structure and bonding. The major development since 1965 in spontaneous, c.w. Raman spectroscopy has been the observation and exploitation by chemists of the resonance Raman effect. This advance, pioneered in chemical applications by Long and Loehr (15a) and by Spiro and Strekas (15b), overcomes the inherently feeble nature of normal (nonresonant) Raman scattering and allows observation of Raman spectra of dilute chemical systems. Because the observation of the resonance effect requires selection of a laser wavelength at or near an electronic transition of the sample, developments in resonance Raman spectroscopy have closely paralleled the increasing availability of widely tunable and line-selectable lasers. 

A complete study of the electronic states of the / configuration of CeClj using the electronic Raman effect has been performed by Kiel eta/, Two pure antisymmetric transitions were observed which are forbidden by normal symmetric tensor selection rules. In this paper the general features of the electronic Raman effect are... 

Different hexaoxometallates have been studied by Hawk (149—152) and by Corsmit et al. (153). Baran and Muller (154) have clearly found by means of IR spectra that Ba5(ReOe)2 contains isolated ReOi octahedra. The known data are collected in Table 20 for different hexaoxometallates however, most of these measurements are incomplete. The IR data for V3 and V4 are only partly correct, since these bands are very broad for some of the lithium salts so that it is often difficult to differentiate between V3, V4, and the v(Li—O) vibrations (755). In most cases it is doubtful whether the IR bands forbidden for the free ion, vi, V2, vs are correctly assigned. Surprisingly enough V3 and V4 do not split in most of the IR spectra even though there is enough perturbation to allow the appearance of normally forbidden transitions. Several hthium hexaoxometallates have been investigated in the Raman effect (755). 

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 ... 

The Raman scattering signal can also be enhanced if one chooses an excitation wavelength corresponding to an electronic transition of the molecule of interest. This resonance Raman effect can enhance the signal by two to six orders of magnitude [55]. Hence, exploiting both the surface enhancement and the molecular resonance leads to extremely low detection limits (e.g., picomolar and below). 

These results apply specifically to Rayleigh, or elastic, scattering. For Raman, or inelastic, scattering the same basic CID expressions apply but with the molecular property tensors replaced by corresponding vibrational Raman transition tensors between the initial and final vibrational states nv and rn . In this way a s are replaced by (mv aap(Q) nv), where aQ/3(<3) s are effective polarizability and optical activity operators that depend parametrically on the normal vibrational coordinates Q such that, within the Placzek polarizability theory of the Raman effect [23], ROA intensity depends on products such as (daaf3 / dQ)0 dG af3 / dQ) and (daaf3 / dQ)0 eajS dAlSf / dQ)0. 

Here, E is the strength of the applied electric field (laser beam), a the polarizability and / and y the first and second hyper-polarizabilities, respectively. In the case of conventional Raman spectroscopy with CW lasers (E, 104 V cm-1), the contributions of the / and y terms to P are insignificant since a fi y. Their contributions become significant, however, when the sample is irradiated with extremely strong laser pulses ( 109 V cm-1) created by Q-switched ruby or Nd-YAG lasers (10-100 MW peak power). These giant pulses lead to novel spectroscopic phenomena such as the hyper-Raman effect, stimulated Raman effect, inverse Raman effect, coherent anti-Stokes Raman scattering (CARS), and photoacoustic Raman spectroscopy (PARS). Figure 3-40 shows transition schemes involved in each type of nonlinear Raman spectroscopy. (See Refs. 104-110.)... 

Suppose that a compound has a Raman-active vibration at vM. If it is illuminated by a probe laser (v) simulataneously with a pump continuum covering the frequency range from v to v + 3,500 cm-1, one observes an absorption at v + vM in the continuum together with emission at v. Clearly, the absorbed energy, h(v + vM), has been used for excitation (/zvM) and emission of the extra energy (hv). This upward transition is called the inverse Raman effect since the normal anti-Stokes transition occurs downward. Because the inverse Raman spectrum can be obtained in the lifetime of the pulse, it may be used for studies of shortlived species (Section 3.5). It should be noted, however, that the continuum pulse must also have the same lifetime as the giant pulse itself. Thus far, the inverse Raman effect has been observed only in a few compounds, because it is difficult to produce a continuum pulse at the desired frequency range. 

The resonance Raman effect was explained by a resonant excitation of the IVCT transition associated with the fivefold-coordinated Mo5+ centers. The Raman scattering intensity results then from the relative efficiencies of the resonant absorption of the incident photons and the resonant reabsorption of the Raman-scattered photons. The resonance enhancement was further demonstrated by investigation of a series of M0O3 v samples with various degrees of reduction (Dieterle and Mestl, 2002 Dieterle et al., 2002). 

Resonance Raman effects, which arise from resonant coupling of the exciting laser light to electronic transitions, can be exploited to overcome difficulties with detection limits and are of particular interest for the characterization of working catalysts that contain reduced transition metal ions. 

---