Transitions Raman-allowed

Recall that homonuclear diatomic molecules have no vibration-rotation or pure-rotation spectra due to the vanishing of the permanent electric dipole moment. For electronic transitions, the transition-moment integral (7.4) does not involve the dipole moment d hence electric-dipole electronic transitions are allowed for homonuclear diatomic molecules, subject to the above selection rules, of course. [The electric dipole moment d is given by (1.289), and should be distinguished from the electric dipole-moment operator d, which is given by (1.286).] Analysis of the vibrational and rotational structure of an electronic transition in a homonuclear diatomic molecule allows the determination of the vibrational and rotational constants of the electronic states involved, which is information that cannot be provided by IR or microwave spectroscopy. (Raman spectroscopy can also furnish information on the constants of the ground electronic state of a homonuclear diatomic molecule.)... 

Recall the mutual exclusion rule stated in Section 6.7. The rule follows from the fact that the integral over all space of an odd ( ) function is zero. The functions x, y, and z belong to u representations of molecules with a center of symmetry, since inversion converts each to its negative. Hence one of the functions vjb and ib must belong to a g representation and one to a u representation if the integrand of (9.189) is not to be odd. Thus only g<->u IR transitions are allowed in molecules with a center of symmetry. In contrast, the functions (9.196) are all even (g), so that for centrosymmetric molecules only g<->g and u u Raman transitions are allowed. This proves the mutual exclusion rule. 

The selection rules are restrictions imposed on the quantum transitions, because of the laws of conservation of angular momentum and parity [59], In the case of IR spectroscopy, within the frame of the harmonic approximation, the applicable rules are the electric dipole selection rules. That is, when the expression in Equation 4.19 has a finite value, the transition is allowed, and when this expression is zero the transition is forbidden. In the Raman case, when one of the integrals given by Equation 4.23 is different from zero, the normal vibration associated is Raman-active. 

In Raman scattering, the excitation light couples to changes in the polarizability and first order transitions are allowed in crystalline silicon. (See Lannin (1984) for a discussion of Raman scattering in amorphous silicon.) The scattering intensity, as a function of the phonon frequency, co, is approximately... 

The typical and much discussed effect of phase transitions is a so-called soft mode, A soft mode is a vibration, the frequency of which nears zero as the physical parameter (mostly the temperature but sometimes also the pressure or the external electric field) approaches its critical point. One of the fir.st soft modes was observed by Raman et al. in the a / quartz transition (Raman and Nedungadi, 1940). The theory of these modes was proposed by Cochran (Cochran, 1960, 1961). It turns out that the soft mode is simply the vibration that, due to its form, allows the transformation from one phase to the other. At the transition point, the restoring forces disappear and the frequency approaches zero. Extensive reviews of the application of spectroscopy in connection with the investigation of phase transitions have been provided by Rao and Iqbal (Rao and Rao, 1978 Iqbal, 1986). 

SAXSAVAXS/RAMAN is especially useful when dealing with chemically induced phase transitions. The example shown in Figure 2(e) is the polymerisation of solvent styrene into polystyrene in which polyethylene is in solution. Polyethylene is soluble in styrene but insoluble in polystyrene. RAMAN allows the determination of the reaction kinetics of polystyrene formation and monitors the crystallisation of the polyethylene. The SAXS monitors the liquid-liquid phase separation followed by the liquid-solid phase transition, whilst the WAXS also observes the liquid solid phase by monitoring the appearance of peaks due to the crystallisation of polyethylene. These are very valuable parameters when trying to define any new manufacturing process. ... 

Figure 4.4 gives the Raman spectrum of trimethylene oxide55. Although the Av = 1 transitions are allowed, the prominent features are the Av = 2 transitions. Since these overtones are totally symmetric, the sharpness of the Q-branches of such Raman transitions accounts for their prominence in the spectrum. 

Since the wavelengths of visible and infrared photons are always large in comparison to the lattice constants, the scattering vector Q can take on only vanishingly small values. Therefore, Raman scattering detects phonons only at K 0, i.e. at the centre F of the first BZ (G = 0). In addition to the conservation laws, symmetry selection rules hold, which take into account the fact that Raman scattering is a two-quantum process. When g and u states are present, it is found for Raman processes that g g transitions are allowed and w g transitions are forbidden. Therefore, the lines in the Raman spectrum can be associated with the symmetry of the excited phonons. 

Infrared Absorption is a single-photon process. Here, also, kiR = K 0 applies. Thus, infrared absorption detects only phonons at the F point of the first BZ. In this case, we have oo = L2, where ho) is the quantum energy of the infrared radiation. The frequencies or the wavenumbers of the optical phonons in molecular crystals are of the order of 3 THz or 100 cm" thus the wavelengths of infrared absorption are of the order of 100 /xm. Infrared spectroscopy of phonons in molecular crystals is therefore in fact far-infrared spectroscopy. The symmetry selection rules are complementary to those for Raman scattering for vibrations with u and g states w g transitions are allowed and g g transitions are forbidden. 

Spontaneous Raman scattering always occurs when the laser excitation frequency is less than the frequency associated with an allowed electronic transition of the molecule. As the probe laser frequency approaches that of an electronic transition in the molecule, certain vibrational modes that couple strongly to the transition increase in intensity (pre-resonance) with respect to other Raman allowed modes of the molecule. When the excitation frequency coincides with the electronic transition frequency (resonance), a dramatic increase in vibrational band intensities is observed. This effect has been observed in many molecules and especially in polymer films, such as polydiacetylene, that consist of extended regions of electron delocalization owing to the presence of conjugated double and triple carbon-carbon bonds in the linear network (40)(41). 

The selection rules for the Raman effect are obtained by replacing P in Eq. 8.37 by the components of induced dipoles. These components a,y are the nine elements of the polarizability tensor, where i, j = x, y, z. The aij form a basis for the same rep as ij, namely T(ij), so that a particular transition is allowed in the Raman effect if F(m) X F(>/) contains T ij). Many more necessary details regarding the intensities of IR and Raman spectra that are beyond the scope of the present work are given by Wilson, Decius, and Cross (5). 

In the case of cubic crystal symmetry the T, and F symmetry components are Raman allowed. In fig. 15 the well known vibrations of the octahedra have been included to demonstrate the corresponding symmetry. The peak near 95 cm appears only in F symmetry with the Tj and F components being zero. The symmetry analysis is consistent with the identification of the 95 cm line as due to a crystal-field excitation, but does not allow a separation of the two transitions. 

The second factor in (2.66) describes quite generally the transition probability for all possible two-photon transitions such as Raman scattering or two-photon absorption and emission. Figure 2.30 illustrates schematically three different two-photon processes. The important point is that the same selection rules are valid for all these two-photon processes. Equation (2.66) reveals that both matrix elements D,- and Dkf must be nonzero to give a nonvanishing transition probability A,/. This means that two-photon transitions can only be observed between two states i) and I/) that are both connected to intermediate levels fe) by allowed single-photon optical transitions. Because the selection rule for single-photon transitions demands that the levels i) and A ) or A ) and /) have opposite parity, the two levels i) and I/) connected by a two-photon transition must have the same parity. In atomic two-photon spectroscopy s s or s d transitions are allowed, and in diatomic homonuclear molecules Eg Eg transitions are allowed. 

Far from resonance, a fundamental (Au = 1) Raman transition is allowed if the normal mode involved corresponds to the same species as one of the components of the scattering tensor, provided this component is not antisymmetric. As we have seen, this last restriction does not apply under resonance conditions. In practice, Raman overtones are usually extremely weak far from resonance although they are not strictly forbidden. Under resonance conditions, they may be strong. 

The transition moments can be identified in the character tables by the Cartesian coordinates in the functions column x, y, or z signify electric dipole transitions, whereas x, xy, or other quadratic terms signify Raman transitions, b. The transition is allowed by symmetry selection rules if the symmetry representation F for the initial state and Fy for the final state obey the relations... 

What Raman and what electric dipole transitions are allowed from one of the A2 electronic states of NH3 ... 

Determine whether the transition — is allowed (a) by electric dipole or (b) by Raman selection rules for the molecule BH3. 

The pure rotation spectrum of an asymmetric top is very complex, and cannot be reduced to a formula giving line positions. Instead, it has to be dealt with by calculation of the appropriate upper and lower state energies (Section 7.2.2). The basic selection rule, A7 = 0, 1, applies to absorption/emission spectra, and there are other selection rules. These depend on the symmetry of the inertial ellipsoid, which is always Dan, but the orientations of the dipole moment components depend on the symmetry of the molecule itself. For the rotational Raman effect A7= 2 transitions are allowed as well. The selection rules for pure rotational spectra are described in more detail in the on-line supplement for Chapter 7. 

Infrared-allowed transitions are dipole-allowed. That is, the (electric) dipole of the incident radiation couples in resonance with a vibration which changes the (electric) dipole of the molecule. So, an infrared-allowed vibration behaves like a dipole and that means like a coordinate axis. In contrast, Raman involves two light waves, one in, the other out. So, Raman selection rules reflect this difference and a vibration which behaves like a product of two dipoles, like a product of coordinate axes, are Raman-allowed. Clearly, infrared and Raman have different selection rules. In the statements above, the word behaves means has the same symmetry properties as . 

The coherent Raman processes are generated when two laser beams, one of which has a tunable frequency, are brought to a common focus in a sample (see Fig. 7), As soon as the frequency difference coi — co 2 of the two lasers corresponds to the frequency (Oj of a Raman-allowed rotation-vibrational transition, a nonlinear interaction with the molecules occurs via the third-order nonlinear susceptibility the corresponding state is... 

In this case the character of the direct product Xaixe( ) is the same as XeW- Whenever an E type fundamental transition is allowed in the infrared and Raman spectrum then the combination band transition involving and E type normal coordinates will also be allowed. 

Verzhbitskiy et reported a collision-induced Raman band by mixtures of sulfur hexafluoride and dinitrogen. A systematic analysis brings forth evidence of double ineoherent seattering (DRS) by this mixture with both moleeules undergoing two Raman-allowed transitions. The band is found to be almost fully depolarized. In a subsequent paper Chrysos and Verzhbitskiy" extraeted the isotropie spectrum of the above-mentioned band. 

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