Vibrational—rotational Raman spectra

As for dipole transitions, we obtain a combined vibrational-rotational spectrum for Raman scattering. Such a Raman band contains three branches, S, Q (AJ=0) and O. Since the rotational constants for the vibrational levels with V = 0 and 1 are almost identical the lines of the Q branch occur almost on top of each other and can frequently not be resolved. Because of this, a very strong central line occurs. The S and O branches are much 

As we have seen, IR and Raman spectra frequently yield the same information. Raman spectra can, in many respects, be considered as IR spectra which have been moved into UiC visible region employing a visible excitation line. However, IR and Raman spectra also complement each other as different transitions can sometimes be observed. 

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We saw that homonuclear diatomic molecules exhibit no pure-rotation or vibration-rotation spectra, because they have zero electric dipole moment for all internuclear separations. The Raman effect depends on the polarizability and not the electric dipole moment homonuclear diatomic molecules do have a nonzero polarizability which varies with varying internuclear separation. Hence they exhibit pure-rotation and vibration-rotation Raman spectra. Raman spectroscopy provides information on the vibrational and rotational constants of homonuclear diatomic molecules. 

Nuclear spin statistical weights were discussed in Section 5.3.4 and the effects on the populations of the rotational levels in the v = 0 states of H2, 19F2, 2H2, 14N2 and 1602 illustrated as examples in Figure 5.18. The effect of these statistical weights in the vibration-rotation Raman spectra is to cause a J" even odd intensity alternation of 1 3 for H2 and 19F2 and 6 3 for 2H2 and 14N2 for 1602, all transitions with J" even are absent. It is for the... 

Figure 6.8-13 Vibrational-rotational Raman spectra of O2 for fixed rotational temperature (300 K) and different vibrational temperatures (1000 K, 2000 K, 3000 K).

HGM Edwards, DA Long, KAB Najm, M Thomsen. The vibration-rotation Raman spectra of Oa,... 

HGM Edwards, DA Long, HR Mansour, KAB Najm. Pure rotation and vibration-rotational Raman spectra of H H and H H. J Raman Spectrosc 8 251-254, 1979. 

HGM Edwards, DW Farwell, AC Gorvin, DA Long. Pure rotational and vibration-rotational Raman spectra of H2, H H and H2. J Raman Spectrosc 17 129-132, 1986. 

M Becucci, E Castellucci, L Fusina, G Di Lonardo, HW Schrotter. Vibration-rotation Raman spectrum of " C-containing acetylene. J Raman Spectrosc 29 237-241, 1998. 

As in the infrared spectrum, overtone bands with Ac > 1 are possible, but have much weaker intensity and are usually not observed.) The A/= -2, 0, and +2 branches of a vibration-rotation Raman band are called O, Q, and S branches, respectively, in an extension of the P, Q, R notation used in infrared spectra. 

Figure 4.3-24 Part of the pure rotational Raman spectrum of CO2 at a pressure of 10 kPa. Slitwidth 0.21 cm, scanning speed 0.2 cm /min, laser power 8 W at 514.5 nm. The S-branch lines of the molecules in the vibrational ground state are off scale (Altmann et al., 1976).

In accordance with these considerations, the pure-rotational Raman spectrum (selection rule AJ= 2) of has every second line missing, whereas that of Na has all lines present, but those arising from even-J states axe more intense than those arising from. odd-J states (2). Yoshino and Bernstein (ll) have observed intensity alternations having statistical origins in both the pure-rotational Raman spectrum of Ha, and in the rotational fine-structure (selection rules AJ=0, 2) of the vibrational band in the Raman spectra of both and Da. 

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]. 

Raman spectra of chlorine, bromine, and iodine gas were first recorded by Holzer et al. [155] with argon laser excitation and the latter two halogens showed a strong resonance Raman effect. Isotope splittings and hot-band structure were observed in the vibrational band of CI2 [56,156]. The pure rotational Raman spectrum of bromine was recorded by Baierl et al. [157] and numerous investigations concentrated on the resonance Raman effect of bromine and iodine for reviews see Refs. 158 and 159. 

This spectrum is called a Raman spectrum and corresponds to the vibrational or rotational changes in the molecule. The selection rules for Raman activity are different from those for i.r. activity and the two types of spectroscopy are complementary in the study of molecular structure. Modern Raman spectrometers use lasers for excitation. In the resonance Raman effect excitation at a frequency corresponding to electronic absorption causes great enhancement of the Raman spectrum. 

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

Figure 6.9 The 1-0 Stokes vibrational Raman spectrum of CO showing the 0-, Q-, and 5-branch rotational structure...

If the resolving capacity of the instruments is ideal then vibrational-rotational absorption and Raman spectra make it possible in principle to divide and study separately vibrational and orientational relaxation of molecules in gases and liquids. First one transforms the observed spectrum of infrared absorption FIR and that of Raman scattering FR into spectral functions... 

The half-width (at half-height) and the shift of any vibrational-rotational line in the resolved spectrum is determined by the real and imaginary parts of the related diagonal element TFor linear molecules the blocks of the impact operator at k = 0,2 correspond to Raman scattering and that at k = 1 to IR absorption. The off-diagonal elements in each block T K, perform interference between correspond-... 

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). 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

The vibration-rotation gas-phase Raman spectrum of C3 O2 was obtained for the first time by Smith and Barrett using a 2-watt argon-ion laser. The results of this experiment gave new information about the bonding potential function for the central carbon bonding fundamental. 

With the available high-power lasers the nonlinear response of matter to incident radiation can be studied. We will briefly discuss as examples the stimulated Raman effect, which can be used to investigate induced vibrational and rotational Raman spectra in solids, liquids or gases, and the inverse Raman effect which allows rapid analysis of a total Raman spectrum. A review of the applications of these and other nonlinear effects to Raman spectroscopy has been given by Schrotter2i4)... 

Rotational Raman spectroscopy is a powerful tool to determine the structures of molecules. In particular, besides electron diffraction, it is the only method that can probe molecules that exhibit no electric dipole moment for which microwave or infrared data do not exist. Although rotational constants can be extracted from vibrational spectra via combination differences or by known correction factors of deuterated species the method is the only one that yields directly the rotational constant B0. However for cyclopropane, the rotational microwave spectrum, recording the weak AK=3 transitions could be measured by Brupacher [20],... 

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