Selection Rules for IR Spectroscopy

For IR spectroscopy, the appropriate operator is the transition dipole moment. This has components with the same symmetry as jc, y and z. The selection rule for IR spectroscopy requires that a vibration must have the same irreducible representation as one of X, y and z. 

In the main text we introduced the selection rules for IR spectroscopy via the transition dipole moment integral. This appendix gives a little more detail on the origin of the selection rules, with explicit formulae for the vibrational wavefunctions. This also allows a more complete explanation of the observation that absorption due to transitions involving neighbouring levels (e.g. n = 0 to n = 1) are more easily observed than overtones which involve transitions to higher levels in the ladder of vibrational states. 

The selection rule for IR spectroscopy is that for absorption to occur, the molecular dipole must change during the course of the vibration. Thus, simple diatomic molecules such as Oj do not absorb. The most intense absorptions involve polar functional groups—carbonyl groups absorb more strongly than alkenes, and nitriles more strongly than alkynes. 

One finds that, in molecules of high symmetry, both IR and Raman spectroscopy are needed to observe the vibrational modes. Even with both techniques, there may still be some vibrations that are totally forbidden. The best known selection rule for IR and Raman spectroscopy is known as the Rule of Mutual Exclusion , which states that if a molecule has a centre of symmetry, vibrations cannot be active in both IR and Raman spectroscopy. This rule has often been applied in molecular structure investigations to determine whether a centre of symmetry is present. In general, vibrations that do not distort the molecular symmetry, symmetric vibrations , are intense in the Raman spectrum while those that maximize the distortion are most intense in the IR spectrum. If the atoms involved in these vibrations are highly polarizable (e.g., sulfur or iodine) then the Raman intensity is high. Some examples of... 

Raman spectroscopy is another form of vibrational spectroscopy that is subject to different selection rules from IR spectroscopy and therefore complementary to it. Raman spectroscopy has, for example, been used to fingerprint the framework region of zeolites (interpreting spectra in terms of characteristic building units, for example) and to investigate the incorporation of transition metals in the framework, such as titanium. Raman spectra of titanosilicates give characteristic resonances at 1125 and 960 cm, for example. 

Inelastic electron tunnelling spectroscopy (lETS) has been used to study some silanes on aluminium oxide. The technique records vibrational spectra of an absorbed monolayer. Silanes can be applied to the oxidised metal from solution or vapour, and devices are completed by evaporation of a top electrode which is usually of lead, because of its superconductivity. The device is cooled to the temperature of liquid helium (4.2 K) to minimise thermal broadening. Most electrons (>99%) pass through the device elastically, but a small number excite vibrational modes. It is these that are detected and displayed as a spectrum. Both IR and Raman modes can be observed the selection rule for lET spectroscopy is one of orientation, in that bonds which are aligned perpendicular to the surface give the most intense peaks. 

The chapter is roughly divided into three sections. In the first (Sections 6.2 and 6.3) we look at the background theory of vibrational spectroscopy, including the selection rules for IR and Raman spectroscopy. We can already use reducible representations and the reduction formula to determine the symmetry labels for the vibrational modes of any molecule. 

In the next two sections we consider the selection rules for IR and Raman spectroscopies in more detail. 

Now g (and g as well) in Eqs. (82)-(85) are functions of frequency, and ratios such as Ll/L are also functions of exciting frequency. To the blue of the localized surface plasmon peak, the ratio L /L progressively decreases, but to the red of the peak, L L] gradually increases. In fact, for metals, since Re(e)- -oo as the excitation frequency approaches the infrared Eq. (83) shows that L - 0 in the infrared, while Eq. (82) shows that V is finite in the infrared. These results are the basis of the surface selection rules for IR surface spectroscopy, where the electric field of the light incident on metals must be concentrated in the normal direction. They also emphasize that the tangential component of the field will decrease with respect to the normal component as the excitation source is moved towards the red region of the visible spectrum. 

Accordingly, the selection rules for Raman and IR spectroscopy are different. In Raman spectroscopy, there must be a change in the molecule s polarizability upon excitation, whereas a change in dipole moment is required for IR. A dipole moment is the magnitude of the electronic force vector between the negative and positive charges or partial charges on a molecule. A permanent dipole moment exists in all polar mol-... 

An alternative experiment that measures the same vibrational fundamentals subject to different selection rules is Raman spectroscopy. Raman intensities, however, are more difficult to compute than IR intensities, as a mixed third derivative is required to approximate the change in the molecular polarizability with respect to the vibration that is measured by the experiment. The sensitivity of Raman intensities to basis set and correlation is even larger than it is for IR intensities. However, Halls, Velkovski, and Schlegel (2001) have reported good results from use of the large polarized valence-triple-f basis set of Sadlej (1992) and... 

The selection rules for the Raman effect are quite different from those for IR spectroscopy. The mechanism involves interaction between the incident radiation and the fluctuating polarisability of the molecule, in contrast to the fluctuating dipole moment in IR absorption. The dipole moment is a vector quantity, and can be resolved into components along three Cartesian axes. The polarisability is a tensor quantity, whose components can be written as products of Cartesian axes. For a molecule having no symmetry at all, or having only a plane of symmetry, all... 

It is always desirable to back up IR absorption spectroscopy with Raman measurements. The different selection rules for the two techniques means that, at least for symmetric species, it is often necessary to have data from both types of measurement to have a full picture of the vibrational spectrum. Raman spectroscopy has been used to study many matrix-isolated species although there are problems regarding intensity and photosensitivity. An excellent review exists on the subject that highlights both the applications and difficulties of the method. A molecule that has been well characterized by both IR and Raman spectroscopy is the matrix-isolated species Mo(C )s(N2) (15). Spectra for (15) are illustrated... 

According to the selection rules, the HRS spectroscopy can in principle be used as an alternative for IR spectroscopy [19]. Indeed, this nonlinear spectroscopy has several advantages IR-mode detection is possible even in IR-opaque media and its spatial resolution is much better than IR microscopy. Moreover, HRS signals appear in the doubled frequency region, which is far from the intense excitation laser line, and hence, low-energy vibration modes are easily observable. 

For the interpretation of the results of the IR and Raman spectroscopy one can use phonon frequencies calculated by using the so-called harmonic approximation widely used in solid-state physics [26]. The selection rules for... 

Molecules with polar groups such as H2O exhibit very strong and often broad absorption bands in IR spectrum whereas they have weak bands in the Raman spectrum. A full theoretical discussion of the selection rules of IR and Raman spectroscopy can be found for example in (Smith 1979 Ferraro and Nakamoto 1994). IR and Raman spectroscopy tend to be complementary techniques. Moreover, both types of spectroscopy are required to measure the complete vibrational spectrum. Both these techniques are well developed, and instruments for carrying out each of the techniques are commercially available. 

Fig. 19.11 The trans- and cis-isomcrs of the square planar complex [PtCl2(NH3)2] can be distinguished by IR spectroscopy. The selection rule for an IR active vibration is that it must lead to a change in molecular dipole moment (see Section 3.7).

Figure 5 shows the SFG vibrational spectra of carbon monoxide obtained at 10 -700 Torr of CO and at 295 K. When the clean Pt(lll) surface was exposed to 10 L (1 L=10 Torr sec) of CO in UHV, two peaks at 1845 cm and 2095 cm were observed which are characteristic of CO adsorbed at bridge and atop sites. LEED revealed that a c(4 X 2) structure was formed in which an equal number of carbon monoxide molecules occupied atop and bridge sites [15]. Such results are in agreement with previous HREELS [16] and reflection-absoiption infrared spectroscopy (RAIRS) [17] studies. ITie much higher relative intensity of atop bonded CO to bridge bonded CO in the SFG spectra is due to the specific selection rule for the SFG process [18]. As mentioned earlier, SFG is a second order, nonlinear optical technique and requires the vibrational mode under investigation to be both IR and Raman active, so that the SFG intensity includes contributions from the Raman polarizability as well as the IR selection mle for the normal mode. 

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