Selection Rules for Infrared Absorption

Most of the sulfur rings have either no or only small dipole moments owing to the low or lacking polarity of the sulfur-sulfur bonds. Therefore, infrared spectra of these species are of low intensity as a result of the selection rule for infrared absorption. In contrast, the Raman scattering intensity of S-S bonds is very strong and Raman spectra are therefore the best technique to study sulfur melts and samples prepared from the melt like r-sulfur and /i-sulfur. In Fig. 1 a schematic comparison is made to demonstrate the differences in the Raman spectra of the homocycles with between 6 and 12 atoms. 

Intramolecular vibrational redistribution (IVR) is an important nonradiative process in an isolated large molecule, and it is being extensively studied experimentally and theoretically. Especially, IVR in electronically excited state has been studied by various experimental means such as fluorescence excitation, dispersed fluorescence spectroscopies and the measurement of fluorescence life-time. As a result, our information on IVR for electronically excited states is now considerably accumulated. On the other hand, the study on IVR in electronically ground-state is very few. This is due to lack of suitable experimental means. The study by infrared radiation is an orthodox way. However, because of poor time response of the infrared detection and of severe selection rule for infrared absorption, the IVR study of a ground state molecule by infrared light is greatly restricted. Instead of direct vibrational excitation by... 

The specific selection rule for infrared absorption spectra is... 

Tensor representations, synonymous for product representations and their decomposition into irreducible constituents, are useful concepts for the treatment of several problems in spectroscopy. Important examples are the classification of the electronic states in atoms and the derivation of selection rules for infrared absorption or the vibrational Raman or hyper-Raman effect in crystals. In the first case the goal is to reduce tensors which are defined as products of one-particle wave functions, while in the second case tensors for the dipole moment, the electric susceptibility or the susceptibilities of higher orders have to be reduced according to the irreducible representations of the relevant point groups. 

For a molecule to show infrared absorptions it must possess a specific feature, i.e. an electric dipole moment of the molecule must change during the vibration. This is the selection rule for infrared spectroscopy. Figure 1.4 illustrates an example of an infrared-active molecule, a heteronuclear diatomic molecule. The dipole moment of such a molecule changes as the bond expands and contracts. By comparison, an example of an infrared-inactive molecule is a homonuclear diatomic molecule because its dipole moment remains zero no matter how long the bond. 

Some characteristics of, and comparisons between, surface-enhanced Raman spectroscopy (SERS) and infrared reflection-absorption spectroscopy (IRRAS) for examining reactive as well as stable electrochemical adsorbates are illustrated by means of selected recent results from our laboratory. The differences in vibrational selection rules for surface Raman and infrared spectroscopy are discussed for the case of azide adsorbed on silver, and used to distinguish between "flat" and "end-on" surface orientations. Vibrational band intensity-coverage relationships are briefly considered for some other systems that are unlikely to involve coverage-induced reorientation. 

The selection rules [118] for infrared absorption and Raman scattering in crystals can be derived by taking into consideration conservation of energy, con-... 

By convention, these are often called infrared selection rules, to distinguish between the selection rules for vibrational spectra obtained by infrared absorption and Raman spectroscopy (described later in this section). We will stick to the more cumbersome electric dipole to avoid the suggestion that the rules are wavelength-dependent. 

Several other forms of nonlinear spectroscopy have been developed that are not strictly based on Raman-active vibrations or rotations. Degenerate four-wave mixing (DFWM) is a technique where all input and output frequencies are identical. Because it does not involve the generation of light at new frequencies, it can rely on non-local mechanisms other than the local electronic polarizability (e.g. electrostric-tion). The selection rules for DFWM are closely related to those of one-photon techniques (e.g. absorption). DFWM using infrared beams is therefore used to probe infrared absorbing transitions instead of Raman-active transitions. 

A.2. Infrared Spectrometry. Theoretical studies of the effect of the degree of crystallinity on vibration spectra account only partially for the appearance or the disappearance of certain absorption bands when comparing amorphous polymers with semicrystalline ones. However, these differences are admittedly related both to the appearance (or the disappearance) of intra- or intermolecular interactions and also to stricter selection rules for the crystalline state. In the latter case, absorption bands corresponding to interactions are better defined and thus narrower they are fewer due to stricter rules of selection. For example, in the case of polyamide-6,6, a linear variation of the intensity of two characteristic absorption bands is observed as a function of the density and hence degree of crystallinity (Figure 6.26). One band is due to the crystalline state, and the other one is due to the amorphous state. 

Four models for water adsorption on a metallic surface can be distinguished (Figure 27b). Due to the surface selection rules and remembering that only the vibrational modes which induce a change in the dipolar component perpendicular to the surface are able to absorb the infrared radiation, it is possible to predict the configurations which are active for infrared absorption (Table Villa). It is seen that configurations A and B absorb only in the symmetric modes, while configuration D absorbs in the antisymmetric mode and a little in the symmetric modes. 

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

---