Spectroscopy selection rules

The complexity of Raman spectra for polymers is reduced as with infrared spectra because vibrations of the same type superimpose. In addition, as with infrared spectroscopy, selection rules aid in determining which molecular vibrations are active. However, the criterion for Raman aetivity is a change in bond polarizability with molecular vibration or rotation in contrast to the infrared criterion of a change in dipole moment (Figure 6.6). This means that, for molecules such as carbon dioxide that show both a change in dipole moment and a change in polarizability,... 

In XAS, the incident X-rays traverse through the sample. X-rays of appropriate energy are absorbed by the atoms and as a result a core electron is excited to unoccupied states above p- The decrease in the transmitted X-ray intensity is measured. In this spectroscopy, selection rules are rigorously obeyed and therefore the DOS of all symmetries must be considered to understand completely the electronic structure of the conduction band. The schematic of this X-ray excitation of a core level atom, in the one-electron approximation, is shown in Figure 1. In the one-electron approximation, the activity of one electron is considered at any instant, assuming all other electrons to be fixed. Because the incident X-rays traverse the whole sample, little surface information is obtained. 

As in the case of absorption and fluorescence emission spectroscopy, selection rules apply for the Raman transitions between rotational energy levels. However, since two photons are involved in the process, each of angular momentum Lphoton = 1. angular momentum conservation requires that the difference between the initial and final rotational levels must be two. As the selection rule for pure Raman spectra, one finds... 

This spectrum is called a Raman spectrum and corresponds to the vibrational or rotational changes in the molecule. The selection rules for Raman activity are different from those for i.r. activity and the two types of spectroscopy are complementary in the study of molecular structure. Modern Raman spectrometers use lasers for excitation. In the resonance Raman effect excitation at a frequency corresponding to electronic absorption causes great enhancement of the Raman spectrum. 

We now turn to electronic selection rules for syimnetrical nonlinear molecules. The procedure here is to examme the structure of a molecule to detennine what synnnetry operations exist which will leave the molecular framework in an equivalent configuration. Then one looks at the various possible point groups to see what group would consist of those particular operations. The character table for that group will then pennit one to classify electronic states by symmetry and to work out the selection rules. Character tables for all relevant groups can be found in many books on spectroscopy or group theory. Ftere we will only pick one very sunple point group called 2 and look at some simple examples to illustrate the method. 

CAHRS and CSHRS) [145, 146 and 147]. These 6WM spectroscopies depend on (Im for HRS) and obey the tlnee-photon selection rules. Their signals are always to the blue of the incident beam(s), thus avoiding fluorescence problems. The selection ndes allow one to probe, with optical frequencies, the usual IR spectrum (one photon), not the conventional Raman active vibrations (two photon), but also new vibrations that are synnnetry forbidden in both IR and conventional Raman methods. 

Perhaps the best known and most used optical spectroscopy which relies on the use of lasers is Raman spectroscopy. Because Raman spectroscopy is based on the inelastic scattering of photons, the signals are usually weak, and are often masked by fluorescence and/or Rayleigh scattering processes. The interest in usmg Raman for the vibrational characterization of surfaces arises from the fact that the teclmique can be used in situ under non-vacuum enviromnents, and also because it follows selection rules that complement those of IR spectroscopy. 

The methyl iodide molecule is studied using microwave (pure rotational) spectroscopy. The following integral governs the rotational selection rules for transitions labeled J, M, K... 

The theory of molecular symmetry provides a satisfying and unifying thread which extends throughout spectroscopy and valence theory. Although it is possible to understand atoms and diatomic molecules without this theory, when it comes to understanding, say, spectroscopic selection rules in polyatomic molecules, molecular symmetry presents a small barrier which must be surmounted. However, for those not needing to progress so far this chapter may be bypassed without too much hindrance. 

Raman spectroscopy can in principle be applied to this problem in much the same manner as infrared spectroscopy. The primary difference is that the selection rules are not the same as for the infrared. In a number of molecules, frequencies have been assigned to combinations or overtones of the fundamental frequency of the... 

For comparison the selection rule for infrared spectroscopy according to both classical and quantum mechanics may be stated ... 

Finally, for the determination of selection rules for rotational spectroscopy it is necessary to find the wavefimcdons for this problem. This subject will be left for further development as given in numerous texts on molecular spectroscopy. 

A further technique exists for the determination of triplet energy levels. This technique, called electron impact spectroscopy, involves the use of inelastic scattering of low-energy electrons by collision with molecules. The inelastic collisions of the electrons with the molecules result in transfer of the electron energy to the molecule and the consequent excitation of the latter. Unlike electronic excitation by photons, excitation by electron impact is subject to no spin selection rule. Thus transitions that are spin and/or orbitally forbidden for photon excitation are totally allowed for electron impact excitation. 

It has long been realised that infrared (IR) spectroscopy would be an ideal tool if applied in situ since it can provide information on molecular composition and symmetry, bond lengths and force constants. In addition, it can be used to determine the orientation of adsorbed species by means of the surface selection rule described below. However, IR spectroscopy does not possess the spatial resolution of STM or STS, though it does supply the simplest means of obtaining the spatially averaged molecular information. 

The three most commonly applied external reflectance techniques can be considered in terms of the means employed to overcome the sensitivity problem. Both electrically modulated infrared spectroscopy (EMIRS) and in situ FTIR use potential modulation while polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS) takes advantage of the surface selection rule to enhance surface sensitivity. 

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