Raman spectra transitions

Qe ec is isotopically independent and can therefore be neglected in the isotope ratio equation. Fundamental vibrational frequencies of the reactant can be estimated for simple molecules from analysis of the infrared and Raman spectra. Transition state vibrations must be calculated from an assumed model. Only in recent years with the advent of high-speed computers have complete calculations for any but the simplest molecules become feasible. More often, the equation is simplified by assuming particular models. 

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

The third common level is often invoked in simplified interpretations of the quantum mechanical theory. In this simplified interpretation, the Raman spectrum is seen as a photon absorption-photon emission process. A molecule in a lower level k absorbs a photon of incident radiation and undergoes a transition to the third common level r. The molecules in r return instantaneously to a lower level n emitting light of frequency differing from the laser frequency by —>< . This is the frequency for the Stokes process. The frequency for the anti-Stokes process would be + < . As the population of an upper level n is less than level k the intensity of the Stokes lines would be expected to be greater than the intensity of the anti-Stokes lines. This approach is inconsistent with the quantum mechanical treatment in which the third common level is introduced as a mathematical expedient and is not involved directly in the scattering process (9). 

Since the vibrational spectra of sulfur allotropes are characteristic for their molecular and crystalline structure, vibrational spectroscopy has become a valuable tool in structural studies besides X-ray diffraction techniques. In particular, Raman spectroscopy on sulfur samples at high pressures is much easier to perform than IR spectroscopical studies due to technical demands (e.g., throughput of the IR beam, spectral range in the far-infrared). On the other hand, application of laser radiation for exciting the Raman spectrum may cause photo-induced structural changes. High-pressure phase transitions and structures of elemental sulfur at high pressures were already discussed in [1]. 

The fourth-order coherent Raman spectrum of a liquid surface was observed by Fujiyoshi et al. [28]. The same authors later reported a spectrum with an improved signal-to-noise ratio and different angle of incidence [27]. A water solution of oxazine 170 dye was placed in air and irradiated with light pulses. The SH generation at the oxazine solution was extensively studied by Steinhurst and Owrutsky [24]. The pump and probe wavelength was tuned at 630 nm to be resonant with the one-photon electronic transition of the dye. The probability of the Raman transition to generate the vibrational coherence is enhanced by the resonance. The efficiency of SH generation is also enhanced. 

The wavenumbers of the observed bands are identical with those of the spontaneous Raman spectrum of the solution and oxazine solid [27]. The impulsive stimulated Raman transition may initiate coherent vibrations in the electronic excited state. However, there was no sign of the excited-state vibrations superimposed on the ground-state bands in the spectrum of Figure 6.3. 

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. 

The number of fundamental vibrational modes of a molecule is equal to the number of degrees of vibrational freedom. For a nonlinear molecule of N atoms, 3N - 6 degrees of vibrational freedom exist. Hence, 3N - 6 fundamental vibrational modes. Six degrees of freedom are subtracted from a nonlinear molecule since (1) three coordinates are required to locate the molecule in space, and (2) an additional three coordinates are required to describe the orientation of the molecule based upon the three coordinates defining the position of the molecule in space. For a linear molecule, 3N - 5 fundamental vibrational modes are possible since only two degrees of rotational freedom exist. Thus, in a total vibrational analysis of a molecule by complementary IR and Raman techniques, 31V - 6 or 3N - 5 vibrational frequencies should be observed. It must be kept in mind that the fundamental modes of vibration of a molecule are described as transitions from one vibration state (energy level) to another (n = 1 in Eq. (2), Fig. 2). Sometimes, additional vibrational frequencies are detected in an IR and/or Raman spectrum. These additional absorption bands are due to forbidden transitions that occur and are described in the section on near-IR theory. Additionally, not all vibrational bands may be observed since some fundamental vibrations may be too weak to observe or give rise to overtone and/or combination bands (discussed later in the chapter). 

Resonance Raman spectroscopy has been applied to studies of polyenes for the following reasons. The Raman spectrum of a sample can be obtained even at a dilute concentration by the enhancement of scattering intensity, when the excitation laser wavelength is within an electronic absorption band of the sample. Raman spectra can give information about the location of dipole forbidden transitions, vibronic activity and structures of electronically excited states. A brief summary of vibronic theory of resonance Raman scattering is described here. 

The structure of the stable germanethione 31 (see reaction 14 in Section V) was characterized by FT-Raman spectrum (i Ge=s 521 cm-1, in good agreement with 518 cm-1 reported for Me2Ge=S), UVV spectrum (/,max = 450 nm, el00, Ge=S n-n transition) and FABMS (field absorption). See also Tables 2 and 353. 

To obtain Raman spectra one needs the trajectories of the pq tensor elements of the chromophore s transition polarizability. Actually, for the isotropic Raman spectrum one needs only the average transition polarizability. This depends weakly on bath coordinates and this, together with the weak frequency dependence of the position matrix element, was included in our previous calculations [13, 98, 121]. For the VV and VH spectra, others have implemented... 

Another explanation for their resonance Raman results could be a change in the zwitterionic nature of the merocyanine isomers in the different solvents which may result in changes in the Raman transition probabilities, or the spectral changes could be due to solvent shifts of the absorption spectrum, resulting in a change in the relative contribution of the different vibrational modes to each resonance Raman spectrum. We note that in the same article, the authors report the transient absorption spectra of the merocyanine forms, which clearly show that the BIPS spectrum in cyclohexane has more discrete vibrational modes than are observed in the polar solvents, which show more spectral broadening. Al-... 

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... 

All nonlinear molecules have 3n — 6 vibrational modes, where n is the number of atoms. Some of these modes arc active in the infrared spectrum, some are active in the Raman spectrum, and others do not give directly observable transitions. Analyses of these spectra usually make use of isotopically substituted molecules to provide additional experimental data, and in recent years, theoretical calculations of vibrational spectra have aided both in making assignments of the observed bands, and in providing initial estimates of force constants.97 Standard methods are available for relating the experimental data to the force constants for the vibrational modes from which they are derived.98... 

There are a few exceptions to the statements of the previous paragraph. The vibrational Raman spectrum of liquid H2 shows rotational fine structure for H2, the rotational levels are widely spaced and intermolecular forces are reasonably small. Certain solids when heated undergo a transition to a solid state in which molecular rotation in the crystal is possible. Solid H2 undergoes such a transition, as shown by the heat-capacity curve see Davidsoriy Section 16-9. 

As well as shifting the expected positions of vibrational bands, Fermi resonance affects their intensities. For example, the wave function of the (02°0) level of C02 has a considerable contribution from the harmonic-oscillator function corresponding to the (10°0) level since the latter is a fundamental level, the transition from the ground level (00°0) to the (02°0) level is much more intense than would be expected for an overtone band. This transition is Raman active, but IR inactive the Raman spectrum of C02 shows two very strong bands at 1285 and 1388 cm-1, corresponding to transitions to the (02°0) and (10°0) levels from the ground level. 

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