Polarizability Raman spectroscopy

Infrared and Raman spectroscopy each probe vibrational motion, but respond to a different manifestation of it. Infrared spectroscopy is sensitive to a change in the dipole moment as a function of the vibrational motion, whereas Raman spectroscopy probes the change in polarizability as the molecule undergoes vibrations. Resonance Raman spectroscopy also couples to excited electronic states, and can yield fiirtlier infomiation regarding the identity of the vibration. Raman and IR spectroscopy are often complementary, both in the type of systems tliat can be studied, as well as the infomiation obtained. 

In fact, each linear polarizability itself consists of a sum of two temis, one potentially resonant and the other anti-resonant, corresponding to die two doorway events, and D, and the window events, and described above. The hyperpolarizability chosen in equation (B1.3.12) happens to belong to the generator. As noted, such tliree-coloiir generators caimot produce Class I spectroscopies (fiill quadrature with tliree colours is not possible). Only the two-colour generators are able to create the Class I Raman spectroscopies and, in any case, only two colours are nomially used for the Class II Raman spectroscopies as well. 

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and ot would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection mle Au = 1 in infrared and Raman spectroscopy to be modified to Au = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

In Raman spectroscopy the intensity of scattered radiation depends not only on the polarizability and concentration of the analyte molecules, but also on the optical properties of the sample and the adjustment of the instrument. Absolute Raman intensities are not, therefore, inherently a very accurate measure of concentration. These intensities are, of course, useful for quantification under well-defined experimental conditions and for well characterized samples otherwise relative intensities should be used instead. Raman bands of the major component, the solvent, or another component of known concentration can be used as internal standards. For isotropic phases, intensity ratios of Raman bands of the analyte and the reference compound depend linearly on the concentration ratio over a wide concentration range and are, therefore, very well-suited for quantification. Changes of temperature and the refractive index of the sample can, however, influence Raman intensities, and the band positions can be shifted by different solvation at higher concentrations or... 

Just as the derivatives of the electric dipole with respect to normal coordinates are important in infrared spectroscopy, so the same derivatives of the polarizability play a role in Raman spectroscopy. 

Raman spectroscopy is an inelastic light scattering experiment for which the intensity depends on the amplitude of the polarizability variation associated with the molecular vibration under consideration. The polarizability variation is represented by a second-rank tensor, oiXyZ, the Raman tensor. Information about orientation arises because the intensity of the scattered light depends on the orientation of the Raman tensor with respect to the polarization directions of the electric fields of the incident and scattered light. Like IR spectroscopy, Raman... 

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. 

Where infrared and Raman spectroscopy are limited to vibrations in which a dipole moment or the molecular polarizability changes, EELS detects all vibrations. Two excitation mechanisms play a role in EELS dipole and impact scattering. 

Raman spectroscopy is an emission technique involving the scatter of absorbed light often in the visible region. Raman bands arise from changes in polarizability in molecules during a vibration. Raman spectroscopy is widely used to monitor compounds that have highly... 

The role of quadmpole polarizabilities is less pronounced. Jens Oddershede, e.g., has studied the quadmpole polarizability of N2 [10]. Furthermore, there are studies which point out the need for calculations of quadmpole polarizabilities, e.g., for the interpretation of spectra obtained by surface-enhanced Raman spectroscopy [42,43]. Generally the interest in multipole polarizabilities increases due to new experimental data. We decided, therefore, to also study how different linear response theory methods perform in the calculation of quadmpole polarizabilities. 

A very interesting field of research covers the spectroscopy of van der Waals molecules in search of more detailed information about the long range potential and the polarizability. Raman spectra of van der Waals dimers in argon have been observed and a vibrational frequency shift for I2-molecules from 213 cm" to 197 cm has been measured for I2 -Ar-complexes. 

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-... 

Raman and IR spectroscopies are complementary to each other because of their different selection rules. Raman scattering occurs when the electric field of light induces a dipole moment by changing the polarizability of the molecules. In Raman spectroscopy the intensity of a band is linearly related to the concentration of the species. IR spectroscopy, on the other hand, requires an intrinsic dipole moment to exist for charge with molecular vibration. The concentration of the absorbing species is proportional to the logarithm of the ratio of the incident and transmitted intensities in the latter technique. 

Other detection modes employed in capillary electromigration techniques include chemiluminescence [69-71], Raman spectroscopy [72,73], refractive index [74,75], photothermal absorbance [76,77], and radioisotope detection [78]. Some of these detection modes have found limited use due to their high specificity, which restricts the area of application and the analytes that can be detected, such as radioisotope and Raman-based detection that are specific for radionuclides and polarizable molecules, respectively. On the other hand, the limited use of more universal detection modes, such as refractive index, is either due to the complexity of coupling them to capillary electromigration techniques or to the possibility of detecting the analytes of interest with comparable sensitivity by one of the less problematic detection modes described above. 

The selection rule for Raman spectroscopy requires a change in the induced dipole moment or polarizability of the molecule, and so it is a complementary technique to infrared which requires a change in the permanent dipole moment. For molecules having a center of inversion, all Raman-active bands are infrared inactive and vice versa. As the symmetry of the molecule is lowered, the coincidences between Raman-active and infrared-... 

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... 

Another type of vibrational spectroscopy, which can be used to study molecules without a changing dipole, is Raman spectroscopy which also involves molecular vibrations and, in this case, an interaction between the molecular polarizability (the ease with which the electron cloud around a molecule can be distorted) and th IR radiation. 

A different selection rule applies -there must be a change in the polarizability during the vibration -so that some bands which are IR inactive are Raman active, e.g. the IR inactive C=C stretch of acetylene is Raman active and appears at 2180 cm .The use of Raman spectroscopy in organic chemistry is rare so it will not be discussed any further here. 

We saw that homonuclear diatomic molecules exhibit no pure-rotation or vibration-rotation spectra, because they have zero electric dipole moment for all internuclear separations. The Raman effect depends on the polarizability and not the electric dipole moment homonuclear diatomic molecules do have a nonzero polarizability which varies with varying internuclear separation. Hence they exhibit pure-rotation and vibration-rotation Raman spectra. Raman spectroscopy provides information on the vibrational and rotational constants of homonuclear diatomic molecules. 

Raman spectroscopy (Section 4.10) aids the study of the vibrations of polyatomic molecules. For a vibration to be Raman active, it must give a change in the molecular polarizability. For many molecules with some symmetry, one or more of the normal modes correspond to no change in... 

Both infrared (IR) and Raman spectroscopy have selection rules based on the symmetry of the molecule. Any molecular vibration that results in a change of dipole moment is infrared active. For a vibration to be Raman active, there must be a change of polarizability of the molecule as the transition occurs. It is thus possible to determine which modes will be IR active, Raman active, both, or neither from the symmetry of the molecule (see Chapter 3). In general, these two modes of spectroscopy are complementary specifically, if a molecule has a center of symmetry, no [R active vibration is also Raman active. 

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