Linear molecules Raman spectrum

Figure 5.15 Rotational Raman spectrum of a diatomic or linear polyatomic molecule...

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-... 

Fig. 6.1. A spectral exchange scheme between components of the rotational structure of an anisotropic Raman spectrum of linear molecules. The adiabatic part of the spectrum is shadowed. For the remaining part the various spectral exchange channels are shown ( - — ) between branches (<— ) within branches.

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). 

Stoicheff investigated the pure rotational Raman spectrum of CS2. The first few lines could not be observed because of the width of the exciting line. The average values of the Stokes and anti-Stokes shifts for the first few observable lines (accurate to 0.02 cm-1) are Ap = 4.96, 5.87, 6.76, 7.64, and 8.50 cm-1, (a) Calculate the C=S bond length in carbon disulfide. (Assume centrifugal distortion is negligible. The rotational Raman selection rule for linear molecules in 2 electronic states is AJ = 0, 2.) (b) Is this an R0 or Re value (c) Predict the shift for the 7 = 0—>2 transition. 

In this paper we will present some examples of the application of resonance Raman spectroscopy to the study of transition metal diatomics. The application of Raman spectroscopy to matrix-isolated metal clusters was first reported by Schulze et al. (] ). Having observed only a single line in the Raman spectrum of Ag3, Schulze concluded that the molecule was linear since a bent triatomic and an equilateral triangular geometry would have, in principle, 3 and 2 Raman-active modes. The evidence, however, is not conclusive since many Czy molecules have very weak asymmetric stretches in the Raman ( ) (for example, the V3 mode of O3 is undetectable in the Raman (3 )). Moreover, the bend (V2) of Ag3 is expected to be a very low-frequency mode, perhaps lower than one can feasibly detect in a matrix Raman experiment. 

Figure 2.2-2 The visible, near, middle and far infrared region of the spectrum drawn in a scale linear in wavenumbers. The infrared (IR) and far-infrared (FIR) spectrum is recorded by absorption of light from a continuous spectrum in the range of A = 2.5. .. 100 pm = i) = 4000. .. 100 cm and A = 100. .. 1000 pm = 100. .. 10 cm". Raman spectra can be excited by monochromatic radiation, emitted by different lasers in the visible (VIS) or near-infrared range (NIR). Molecules emit Raman lines with a frequency difference AF to that of the exciting frequency >o between 0 and -f 4000 or - 4000 cm. Usually only the Raman spectrum which is shifted to. smaller wavenumbers, the Stokes Raman spectrum, is recorded. Its range is indicated by bars for different exciting lines Ar" " laser at 488 and 515 nm, HeNe laser at 623 nm, GaAs laser at 780 nm, and Nd YAG laser at 1064 nm.

In the infrared spectrum of polyethylene (Fig. 4.1-2A) this band is split into a doublet at 720 and 731 cm This factor group splitting (Fig. 2.6-1 and Sec. 2.7.6.4) is a result of the interaction between the molecules in crystalline lattice areas. It may be used to investigate the crystallinity of polymers (Drushel and Iddings, 1963 Luongo, 1964). Polyethylene has a unit cell of the factor group Dih (compare Secs. 2.7.5 and 2.7.6.3) which contains a -CH2-CH2- section of two neighboring chains. Each of these sections has a center of inversion in the middle of the C-C bond (Fig. 4.1-3). Therefore the rule of mutual exclusion (Sec. 2.7.3.4) becomes effective The vibrations of the C-C bonds cannot be infrared active and further there are no coincidences of vibrational frequencies in the infrared and Raman spectrum of linear polyethylene. 

In the case of a linear AB2 molecule, two absorptions Vas, 6) should be observed in the IR and one vs) in the Raman spectrum. Corresponding spectra were obtained for noble gas dihalides ... 

The most common protic solvent is water. It is also one of the most complex from the point of view of vibrational spectroscopy because of its highly structured nature. Since water is a triatomic, non-linear molecule it has three vibrational modes, which are illustrated in fig. 5.13. The Vj mode is the symmetrical stretch V2 is the bending mode and V3 is the asymmetrical stretch. All three vibrational modes for water are active in the infrared because they involve changes in the dipole moment. Activity in the Raman spectrum requires that the polarizability of the molecule changes during vibration. Analysis of this aspect of molecular properties is more difficult but it shows that all three modes are also Raman active. A summary of the frequencies of these vibrations for H2O, and the isotopes D2O, and HOD determined from gas phase spectra are given in table 5.7. 

What are the consequences of these considerations for depolarized light scattering In a dilute gas where reorientation is predominantly inertial, we expect the spectrum to be what is normally called the pure rotational Raman spectrum of the molecule. As higher densities are approached, the discrete spectral lines broaden and overlap to form a continuous band. We show how the band shape can be computed for freely rotating linear molecules and spherical top molecules and then indicate the assumptions that have been used by several authors to include collisions in the theory. 

Table Il-2e lists the vibrational frequencies of iriaiomic interhalogeno compounds. The resonance Raman spectrum of the I3 ion gives a series of overtones of the v vibration. - The resonance Raman. spectra of the l2Br" and IBri ions and their complexes with amylose have been studied. The same table also lists the vibrational frequencies of XHY-type (X, Y halogens) compounds. All these species are linear except the ClHCl" ion, which was found to be bent in an inelastic neutron scattering (INS) and Raman spectral studySalt-molecule reactions such as CsF+Fj=Cs[F3] have been utilized to produce a number of novel triaiomic and other anions in inert gas matrices.

The same rules for number of bands in a spectrum apply to Raman spectra as well as IR spectra 3N—6 for nonlinear molecules and 3N—5 for linear molecules. There may be fewer bands than theoretically predicted due to degeneracy and nonactive modes. Raman spectra do not usually show overtone or combination bands they are much weaker than in IR. A rule of thumb that is often tme is that a band that is strong in IR is weak in Raman and vice versa. A molecule with a center of symmetry, such as CO2, obeys another rule if a band is present in the IR spectrum, it will not be present in the Raman spectrum. The reverse is also true. The detailed explanation for this is outside the scope of this text, but the rule explains why the symmetric stretch in carbon dioxide is seen in the Raman spectrum, but not in the IR spectrum, while the asymmetric stretch appears in the IR spectrum but not in the Raman spectmm. 

Methane, CH4, is the most important representative of the regular tetrahedral structure. That it has a centre of symmetry is supported by its vanishing dipole moment and the absence of a rotational spectrum. Just as for linear molecules with a centre of symmetry we have for any other molecules with a centre of symmetry, that the normal vibrations symmetrical with respect to this centre are inactive in emission or absorption. The very strong frequency 2915 cm which only appears in the Raman spectrum must hence be identified with one of the normal vibrations v(s), 8 (s). More particularly it can be proved to be the vibration v (s) in which the outside atoms move in a radial direction with respect to the central atoms. The reason for this identification is the absence of rotational structure in the Raman line, in harmony with the circumstance that the rotation of the molecule vibrating in the way described will not affect its polarisability. Another frequency appearing both in the Raman and infra-red spectrum has the value 3022 cm and must be identified with v a). 

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]. 

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