Raman scattering rules

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

In a diatomic or linear polyatomic molecule rotational Raman scattering obeys the selection rule... 

Because Raman scattering is also a two-photon process the selection rules for two-photon absorption are the same as for vibrational Raman transitions. For example, for a two-photon electronic transition to be allowed between a lower state j/" and an upper state... 

Numerous SERS studies of adsorbed molecules have appeared in the literature. Obviously, it is a useful method for the identification of species at the interface, and its inherent surface sensitivity is an attractive feature. In this context it should be noted that the adsorption of a molecule can change the selection rules for Raman scattering, and modes that are Raman inactive in the isolated molecule may show up in SERS. 

Unfortunately, the different selection rules that apply to resonant and normal Raman scattering were not taken into account in this spectral interpretation. In the following, it is shown that the conclusions and assignments mentioned above have to be modified on the basis of symmetry considerations as discussed by Ricchiardi et al. (41). 

Infrared, Raman, microwave, and double resonance techniques turn out to offer nicely complementary tools, which usually can and have to be complemented by quantum chemical calculations. In both experiment and theory, progress over the last 10 years has been enormous. The relationship between theory and experiment is symbiotic, as the elementary systems represent benchmarks for rigorous quantum treatments of clear-cut observables. Even the simplest cases such as methanol dimer still present challenges, which can only be met by high-level electron correlation and nuclear motion approaches in many dimensions. On the experimental side, infrared spectroscopy is most powerful for the O—H stretching dynamics, whereas double resonance techniques offer selectivity and Raman scattering profits from other selection rules. A few challenges for accurate theoretical treatments in this field are listed in Table I. 

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. 

This was first investigated by Huang n). Long-wave optical phonons are those with small k values. A polar phonon is an infrared-active phonon. Polar phonons therefore can only be observed in the Raman effect for crystals having no center of symmetry in the elementary cell. For centro-symmetric crystals the rule of mutual exclusion applies infrared-active phonons are forbidden in Raman scattering and vice versa. The elementary cells of NaCl and LiF have a center of symmetry, but GaP has none. The following considerations may therefore be applied to GaP as an example. This crystal has two atoms in the elementary cell and is cubic. It can be treated as an optically isotropic medium. 

The selection rules for fi hyper-Raman scattering were derived by Cyvin, Rauch, and Decius, 02) and those for y hyper-Raman scattering, which has not yet been detected experimentally, by Christie and Lockwood 103>. From their tables one can see that silent modes become 3-active for such important point groups as C6, D6, C3v, C6v, C. D, 0 and Oh. Examples of additional 7 activity can be found in the point groups C4v, C. D. D, and Oh. Long and Stanton 104) have derived a quantum-mechanical theory of the hyper-Raman effect which indicates several possibilities for resonance enhancement of hyper-Raman intensities. Iha and Woo 105) extended the theory of nonlinear... 

X lT + E r Xij ki, which refer in their order of appearance to the Cartesian polarization components of the CRS, pump, probe, and Stokes fields in the four-wave mixing process [31]. In transparent and optically inactive media, where the input frequencies are away from any electronic transition frequencies, and only the molecular ground state is populated, the selection rules of both resonant coherent and spontaneous Raman scattering are identical... 

Some surfaces geometries (rough surfaces) concentrate the electric fields of Raman scattering cross section so that it is surface-sensitive. This gives information on surface vibrational modes, and some information on geometry via selection rules. 

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