Symmetry infrared transitions

The allowed changes in the rotational quantum number J are AJ = 1 for parallel (2 ) transitions and A7= 0, 1 for perpendicular (II ) transitions. Parallel transitions such as for acetylene thus have P i J= 1) and R(AJ = +1) branches with a characteristic minimum between them, as shown for diatomic molecules such as HCl in Fig. 37-3 and for the HCN mode in Fig. 2. However, perpendicular transitions such as Vs for acetylene and V2 for HCN (Fig. 2) have a strong central Q branch (AJ = 0) along with P and R branches. This characteristic PQR-Yersus-PR band shape is quite obvious in the spectrum and is a useful aid in assigning the symmetries of the vibrational levels involved in the infrared transitions of a hnear molecule. 

The problems of peak assignment in infrared spectroscopy are probably greater than those faced in analogous NMR experiments. Furthermore, infrared transition probabilities are highly variable owing to symmetry considerations and other molecular properties. In the absence of calibration, relative intensities of infrared absorption bands do not accurately reflect relative concentrations. By characterizing the infrared properties of appropriate model compounds and... 

Furthermore, we have to remark that Group Theory for Non-Rigid Molecules may be advantageously used to deduce a symmetry adapted analytical form for the potential, as well as the symmetry eigenvectors for simplifying the Hamiltonian matrix solution. In the same way. Group Theory permits to label and classify the energy levels and the vibrational functions. Finally, it may be also used to deduce selection rules for the infrared transitions. 

Here Uab is the Raman transition moment, fic is the infrared transition moment, g and V refer to ground and excited vibrational states, coir is the input infrared frequency, coq is the resonance frequency of the adsorbate, and T is a damping factor [8, 14—17]. Thus, the SFG intensity is related to the product of an (anti Stokes) Raman transition and an infrared transition. The SFG intensity is enhanced when the input infrared wavelength coincides with a vibrational mode of the adsorbate and the result of an SFG spectrum corresponds to the vibrational levels of the molecule. This situation is shown schematically in Fig. 5.1. From (5), non-zero SFG intensity will occur only for transitions that are both Raman and IR allowed. This situation occurs only for molecules lacking inversion symmetry [19]. 

There are four electronic transitions (Og symmetry) which should be observed in these systems, and three optical and/or near-infrared transitions between the J = 5/2 and J = 7/2 states have been reported for all the above complexes. In some cases the F7-Fg transition of the J = 5/2 state which occurs in the infrared or near-infrared region has also been observed. These electronic absorption data plus the EPR data on the ground state allow the parameters (including orbital reduction factors) of the Eisenstein-Pryce model [19,35,38] for an octahedral F system to be evaluated as shown in Table 18.1. 

It is also generally true that for molecules without centers of symmetry most transitions occur in both the Raman and the infrared spectra. Groups such as O, and D jh form the only exceptions to this rule. 

We see from (9.12) that initial and final states are connected by two-photon transitions which implies that both states have the same parity. For example, the vibrational transitions in homonuclear diatomic molecules, which are forbidden for single-photon infrared transitions, are accessible to Raman transitions. The matrix elements depend on the symmetry characteristics... 

The symmetry selection rule may also be mqiressed in alternative ways. An infrared transition is not forbidden only in the case where the direct product of the presentations of the two interacting states Fy,xFy. coincides with the representation of at least one of the dipole moment Cartesian components. For a fundamental transition = 1, Vk = 0) the above requirement concerns the irreducible representation of die excited level (V). The selection rule for such transitions is simply... 

Infrared Spectroscopy. The infrared spectroscopy of adsorbates has been studied for many years, especially for chemisorbed species (see Section XVIII-2C). In the case of physisorption, where the molecule remains intact, one is interested in how the molecular symmetry is altered on adsorption. Perhaps the conceptually simplest case is that of H2 on NaCl(lOO). Being homo-polar, Ha by itself has no allowed vibrational absorption (except for some weak collision-induced transitions) but when adsorbed, the reduced symmetry allows a vibrational spectrum to be observed. Fig. XVII-16 shows the infrared spectrum at 30 K for various degrees of monolayer coverage [96] (the adsorption is Langmuirian with half-coverage at about 10 atm). The bands labeled sf are for transitions of H2 on a smooth face and are from the 7 = 0 and J = 1 rotational states Q /fR) is assigned as a combination band. The bands labeled... 

If the vibration does not produee a modulation of the dipole moment (e.g., as with the symmetrie streteh vibration of the CO2 moleeule), its infrared intensity vanishes beeause 0 i/3Ra) = 0. One says that sueh transitions are infrared "inaetive". 

Although we have been able to see on inspection which vibrational fundamentals of water and acetylene are infrared active, in general this is not the case. It is also not the case for vibrational overtone and combination tone transitions. To be able to obtain selection mles for all infrared vibrational transitions in any polyatomic molecule we must resort to symmetry arguments. 

As we proceed to molecules of higher symmetry the vibrational selection rules become more restrictive. A glance at the character table for the point group (Table A.41 in Appendix A) together with Equation (6.56) shows that, for regular tetrahedral molecules such as CH4, the only type of allowed infrared vibrational transition is... 

Having assigned symmetry species to each of the six vibrations of formaldehyde shown in Worked example 4.1 in Chapter 4 (pages 90-91) use the appropriate character table to show which are allowed in (a) the infrared specttum and (b) the Raman specttum. In each case state the direction of the transition moment for the infrared-active vibrations and which component of the polarizability is involved for the Raman-active vibrations. 

The CO2 laser is a near-infrared gas laser capable of very high power and with an efficiency of about 20 per cent. CO2 has three normal modes of vibration Vj, the symmetric stretch, V2, the bending vibration, and V3, the antisymmetric stretch, with symmetry species (t+, ti , and (7+, and fundamental vibration wavenumbers of 1354, 673, and 2396 cm, respectively. Figure 9.16 shows some of the vibrational levels, the numbering of which is explained in footnote 4 of Chapter 4 (page 93), which are involved in the laser action. This occurs principally in the 3q22 transition, at about 10.6 pm, but may also be induced in the 3oli transition, at about 9.6 pm. 

For a fundamental transition to occur by absorption of infrared dipole radiation, it is necessary that one or more of these integrals (and consequently the intensity) be nonzero. It follows from the selection rule given above that in order that a transition be infrared active p must have the same symmetry properties as at least one of x, y, or z. 

The band at 1600 cm-1 due to a double-bond stretch shows that chemisorbed ethylene is olefinic C—H stretching bands above 3000 cm-1 support this view. Interaction of an olefin with a surface with appreciable heat suggests 7r-bonding is involved. Powell and Sheppard (4-1) have noted that the spectrum of olefins in 7r-bonded transition metal complexes appears to involve fundamentals similar to those of the free olefin. Two striking differences occur. First, infrared forbidden bands for the free olefin become allowed for the lower symmetry complex second, the fundamentals of ethylene corresponding to v and v% shift much more than the other fundamentals. In Table III we compare the fundamentals observed for liquid ethylene (42) and a 7r-complex (43) to those observed for chemisorbed ethylene. Two points are clear from Table III. First, bands forbidden in the IR for gaseous ethylene are observed for chemisorbed ethyl-... 

The phthalocyanines, naphthalocyanines, and certain of their metal derivatives (Figure 6.17) are infrared fluorophores. 61"64 As a class, they are exceptionally stable compounds, with copper (Cu) phthalocyanine (not a fluorophore) remaining intact above 300 °C in air. First used for textile dyeing in the last century and still widely used, there is a rich chemistry of phthalocyanines. Most derivatives can be made by prolonged heating of a phthalimide or phthalic acid derivative with a metal in powder or salt form at elevated temperature. Several derivatives absorb in the near-IR, and either fluoresce or phosphoresce. The electronic transitions of phthalocyanines are complex and have been extensively studied, at least in part because the symmetry of the molecule makes theoretical calculations of its spectroscopic behavior more tractable. Unsubstituted phthalocyanines and naphthalocyanines are, as a class, very insoluble in solvents other than, for instance, nitrobenzene. Sulfonated phthalocyanines are water soluble and exhibit spectra comparable to the parent derivative. Photolumines-cent phthalocyanines (Pcs) include SiPc, ZnPc, and PC itself. These compounds have been little used for practical infrared fluorometry to date however, Diatron Corpora-... 

A normal mode of vibration is said to be infrared active if the fundamental transition, in which the mode is excited by one quantum of vibrational energy, is allowed. Initial and final states are described by vibrational wave functions, of which the ground state wave function has Ai symmetry and the excited state has the same symmetry as the normal mode. Thus the fundamental transition... 

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