Selection rules for vibrational spectroscopy

We can use a ratio similar to the one used in Example 14.12, in terms of the reduced masses of the molecules, and use the wavenumber value directly  

Considering the O-H and O-D bonds, the reduced masses (in units of grams per mole) substituted into the above expression yield 

Experimentally in the vibrational spectrum of D2O, the symmetric O-D stretch has a vibrational frequency of 2671 cm which shows that the diatomic approximation applied to parts of molecules can be very good. Such approximate calculations are useful in understanding vibrational spectra of molecules. 

You can verify that these are the appropriate reduced masses. 

As with rotational spectroscopy, there are several ways of stating selection rules for spectral transitions involving vibrational states of molecules. There is a gross selection rule, which generalizes the appearance of absorptions or emissions involving vibrational energy levels. There is also a more specific, quantum-number-based selection rule for allowed transitions. Finally, there is a selection rule that can be based on group-theoretical concerns, which were not considered for rotations. 

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This result is tremendously useful, it not only leads to selection rules for vibrational spectroscopy but also, as was the case with electronic wavefunctions (see 8-2), allows us to predict from inspection of the character table the degeneracies and symmetries which are allowed for the fundamental vibrational wavefunctions of any particular molecule. 

Fortunately, molecular symmetry can help us, for 2.1, 2. Ill and 2.IV have different rotational axes and mirror planes. We will see in due course that this can affect the selection rules for vibrational spectroscopy techniques, which in turn affect how many peaks we would expect to observe in the spectra of the various forms. Symmetry also changes the numbers of equivalent atoms we have in a molecule, and this influences the number of peaks we would observe in, for example, a NMR spectrum. 

This mutual exclusion rule for molecules with a center of symmetry is one example of the manner in whieh symmetry within a molecule can influence the selection rules for vibrational spectroscopy. All elements of symmetry influence the selection rules. The selection rules can be evaluated by using the structural models of the molecules, and the proper structural model for a molecule can be determined by comparing the experimental results with the theoretical resrrlts. This approach to structure determination has been a valuable tool for the study of the various geometric structures of low-molecular-weight substances. This approach can also be used in the study of polymer conformation. 

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. 

Both infrared and Raman spectra are concerned with measuring molecular vibration and rotational energy changes. However, the selection rules for Raman spectroscopy are very different from those of infrared - a change of polarisability... 

The considerations on the symmetries of the ground and excited states and the above conditions lead to the selection rule for infrared spectroscopy A fundamental vibration will be infrared active if the corresponding normal mode belongs to the same irreducible representation as one or more of the Cartesian coordinates. 

In addition to the Raman selection rules described above there are surface selection rules that apply for SERS because the process occurs close to metal surfaces [40—42]. The SERS surface selection rule predicts that the vibrational bands that have contributions from the Raman polarizability tensor component where z is the surface normal, will be most intense with weaker contributions from vibrational bands which have contributions from and o. This is essentially because tlic electric field of the exciting hght is enhanced in the direction of the surface normal (Figure 6.2). The surface selection rule for Raman spectroscopy is more complex than that for infrared spectroscopy. Modes with the bond axis paraUel to... 

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. 

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. 

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. 

Now we turn to vibrational Raman spectroscopy, in which the incident photon leaves some of its energy in the vibrational modes of the molecule it strikes or collects additional energy from a vibration that has already been excited. The gross selection rule for vibrational Raman transitions is that the molecular polarizability must change as the molecule vibrates. The polarizability plays a role in vibrational Raman spectroscopy because the molecule must be squeezed and stretched by the incident radiation in order that a vibrational excitation may occur during the photon-molecule collision. Both homonuclear and heteronuclear diatomic molecules swell and contract during a vibration, and the control of the nuclei over the electrons, and hence the molecular polarizability, changes too. Both types of diatomic molecule are therefore vibrationally Raman active. It follows that the information available from vibrational Raman spectra adds to that from infrared 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. 

Equation (A8.6) shows that the Stokes/anti-Stokes lines depend on the change of molecular polarizability Aa for the vibrational modes of the molecule. This allows us to develop the selection rules for Raman spectroscopy in Section 6.2.4. 

A particularly salient example of the complementarity of normal Raman spectroscopy with other techniques is expressed in a recent publication of the combined data from infrared, normal Raman, SERS, SEHRS, and theoretical predictions for one molecule. First, ab initio theoretical predictions were made for the vibrational characteristics of fran5-l,2-bis(4-pyridyl)ethylene (BPE) at the Hartree-Fock 6-31G level. When the spectra were collected, comparisons were made between the theoretical and experimental results as well as among the different spectra. Based on the known selection rules for each spectroscopy and the matching of wavenumber shifts to theoretical predictions, all vibrational bands were assigned. 

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. 

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. 

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. 

Beyond such electronic symmetry analysis, it is also possible to derive vibrational and rotational selection rules for electronic transitions that are El allowed. As was done in the vibrational spectroscopy case, it is conventional to expand i j (R) in a power series about the equilibrium geometry of the initial electronic state (since this geometry is more characteristic of the molecular structure prior to photon absorption) ... 

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 cross-section in Eq. (1 illustrates another distinguishing feature of inelastic neutron scattering for vibrational spectroscopy, i.e., the absence of dipole and polarizability selection rules. In contrast, it is believed that in optical and inelastic electron surface spectroscopies that a vibrating molecule must possess a net component of a static or induced dipole moment perpendicular to a metal surface in order for the vibrational transition to be observed ( 7,8). This is because dipole moment changes of the vibrating molecule parallel to the surface are canceled by an equal image moment induced in the metal. 

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