Symmetrical molecules vibrations

As for diatomic molecules (Section 7.2.5.2) fhe vibrational (vibronic) transitions accompanying an electronic transition fall into the general categories of progressions and sequences, as illustrated in Figure 7.18. The main differences in a polyatomic molecule are that there are 3A — 6 (or 3A — 5 for a linear molecule) vibrations - not just one - and that some of these lower the symmetry of the molecule as they are non-totally symmetric. 

The fine structure of torsion-vibration spectra of small symmetric molecules and groups such as CH3, CH4, NH3, and NH4 is one of the most illustrative manifestations of tunneling. This problem has been discussed in detail in several reviews and books (see, e.g., Press [1981], Heidemann et al.[1987]). 

Centrosymmetric molecules represent a limiting case as far as molecular symmetry is concerned. They are highly symmetric molecules. At the other extreme, molecules with very low symmetry should produce a set of Raman frequencies very similar to the observed set of infrared frequencies. Between these two extremes there are cases where some vibrations are both Raman and infrared active and others are active in Raman or infrared but not in both. Nitrate ion is an example of a molecule in this intermediate class. 

There are, at present, two overriding reasons an experimentalist would choose to employ laser Raman spectroscopy as a means of studying adsorbed molecules on oxide surfaces. Firstly, the weakness of the typical oxide spectrum permits the adsorbate spectrum to be obtained over the complete fundamental vibrational region (200 to 4000 cm-1). Secondly, the technique of laser Raman spectroscopy is an inherently sensitive method for studying the vibrations of symmetrical molecules. In the following sections, we will discuss spectra of pyridine on silica and other surfaces to illustrate an application of the first type and spectra of various symmetrical adsorbate molecules to illustrate the second. 

Each normal mode of vibration can be described by a normal coordinate Qi which is a linear combination of nuclear displacement coordinates of the molecule. For the symmetric stretching vibration vi of C02, the normal coordinate is of the form... 

The 520 nm absorption of S4 has also been observed in the spectrum of certain red-colored ultramarine samples [21] the assignment of this band to the C2V isomer of 4is supported by the simultaneously observed Raman line at 678 cm which represents the symmetrical stretching vibration of the terminal SS bonds of this molecule (see Table 1 below). 

The wavenumber of the totally symmetric bending vibration, dsss> of S rings (n = 6, 7, 9, 10, 12), on the other hand, is mainly a function of the ring size and not a function of the quite different bond angles in these molecules, as one may expect. The empirically obtained relation is given by... 

It is apparent from Fig. 4 that the normal modes of vibration of the water molecule, as calculated from the eigenvectors, can be described approximately as a symmetrical stretching vibration (Mj) and a symmetrical bending vibration... 

As in infrared spectroscopy, not all vibrations are observable. A vibration is Raman active if it changes the polarizability of the molecule. This requires in general that the molecule changes its shape. For example, the vibration of a hypothetical spherical molecule between the extremes of a disk-shaped and a cigar-shaped ellipsoid would be Raman active. We recall that the selection rule for infrared spectroscopy was that a dipole moment must change during the vibration. As a consequence the stretch vibrations of for example H2 (4160.2 cm"1), N2 (2330.7 cm-1) and 02 (1554.7 cm"1) are observed in Raman spectroscopy but not in infrared. The two techniques thus complement each other, in particular for highly symmetrical molecules. 

Halonen, L. (1987), Rotational Energy Level Structure of Stretching Vibrational States in Some Small Symmetrical Molecules, /. Chem. Phys. 86, 588. 

Figure 4. Schematic illustration of force-constant parameters used in Modified Urey-Bradley Force-Field (MUBFF) vibrational modeling (Simanouti (Shimanouchi) 1949). The MUBFF is a simplified empirical force field that has been used to estimate unknown vibrational frequencies of molecules and molecule-like aqueous and crystalline substances. Here, three force constants (K, H, and describe distortions of a tetrahedral XY molecule, [Cr04] due to bond stretching (Cr-O), bond-angle bending (Z O-Cr-O), and repulsion between adjacent non-bonded atoms (0..0). Less symmetric molecules with more than one type of bond or unequal bond angles require more parameters, but they will belong to the same basic types.

Coriolis operator spect An operator which gives a large contribution to the energy of an axially symmetric molecule arising from the interaction between vibration and rotation when two vibrations have equal or nearly equal frequencies. kor-e o-los, ap-3,rad-3r ... 

If the vibration does not produce a modulation of the dipole moment (e.g., as with the symmetric stretch vibration of the CO2 molecule), its infrared intensity vanishes because (3 l/3R i) = 0. One says that such transitions are infrared "inactive". 

The symmetrical stretching vibration in (1) above is inactive in the IR since it produces no change in the dipole moment of the molecule. The bending vibrations in (3) and (4) above are equivalent and are the resolved components of bending motion oriented at any angle to the internuclear axis they have the same frequency and are said to be doubly degenerate. 

We encounter here for the first time the occurrence of a normal vibration which is completely inactive as a fundamental. This phenomenon is not commonplace but is encountered occasionally in relatively symmetrical molecules. 

Both the Raman and the infrared spectrum yield a partial description of the internal vibrational motion of the molecule in terms of the normal vibrations of the constituent atoms. Neither type of spectrum alone gives a complete description of the pattern of molecular vibration, and, by analysis of the difference between the Raman and the infrared spectrum, additional information about the molecular structure can sometimes be inferred. Physical chemists have made extremely effective use of such comparisons in the elucidation of the finer structural details of small symmetrical molecules, such as methane and benzene. But the mathematical techniques of vibrational analysis are. not yet sufficiently developed to permit the extension of these differential studies to the Raman and infrared spectra of the more complex molecules that constitute the main body of both organic and inorganic chemistry. 

Fig. 31. The scheme of the doublet splitting of the fully symmetric deformational vibration of the ammonia molecule.

---