Intensity of Raman Scattering

Ac x rding to the quantum mechanical theory of light scattering, the intensity per unit solid angle of scattered light arising from a transition between states m and n is given by 

Since the electric dipole operator acts only on the electronic wave functions, the term in Eq. 20.2 can be written in the form  

Here v g corresponds to the energy of a pure electronic transition between the ground and excited states. 

To discuss the Raman scattering, we expand the ( p y)gg term as a Taylor series with respect to the normal coordinate Q  

The first term on the right-hand side is zero unless i = j. This term is responsible for Rayleigh scattering. The second term determines the activity of fundamental vibrations in Raman scattering it vanishes for a harmonic oscillator unless J = l. 

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The intensities of Raman scattering depend on the square of the infinitesimal change of the polarizability a with respect to the normal coordinates, q. Since the polarizability itself is already the second derivative of the energy with respect to the electric field - see equa-... 

Fig. 1. The basic ROA experiment measures a small difference in the intensity of Raman scattering from chiral molecules in right- and left-circularly polarized incident light. Reprinted from Barron et al., 2000, Prog. Biophys. Mol. Biol. 73,1-49, with permission from Elsevier Science.

The first term on the right-hand side of Equation (1.24) accounts for the generated intensity due to Rayleigh scattered light, while the second term is related to the intensity of the Raman scattered light. For visible light coo 10 Hz, while the characteristic phonon frequencies are much shorter, typically 12 10 Hz. Then coq and the intensity of Raman scattering varies as coq, as stated in point (iv) above. 

The intrinsically low intensity of Raman scattering strongly influences both the sensitivity and penetration depth of SORS and its variants. Dominant noise components (photon shot noise or thermal/dark count [1]) can be minimised relative to signal by increasing absolute signal levels. In many Raman systems, collection optics, laser power and other relevant parameters are usually maximised for optimum performance of the system current detectors (CCD devices), for example, have detection efficiencies approaching 100%. Typically, acquisition time provides the only straightforward means available... 

In general, the intensity of Raman scattering increases as the (da/dq)0 becomes larger. 

A third way (Creighton, 1988) in which the surface may modify the intensity of Raman scattering by molecules adsorbed at the surface is by perturbing the molecules as a result of the bonding interaction with the surface. However, it turned out that this chemical effect on the Raman spectra is relatively small, and it is not normally considered to be a part of SERS, though it is inseparable from it. Several other SERS mechanisms have also been proposed (see for instance the discussion by Moskovits, 1985) which by now are widely thought to make at most only minor contributions to the enhancements observed in SERS. 

The intensity of Raman scattering depends strongly on the excitation frequency. Fignre 11 illnstrates what happens if,... 

Moskovits M (1978) Surface-roughness and enhanced intensity of Raman-scattering by molecules adsorbed on metals. J Chem Phys 69(9) 4159-4161... 

Raman optical activity (RO A) Due to molecular chirality there is a difference in the intensity of Raman scattered right and left circularly polarized light. Raman optical activity (ROA) is a vibrational spectroscopic technique that is reliant on this difference and the spectrum of intensity differences recorded over a range of wavenumbers reveals information about chiral centers within a sample molecule. It is a useful probe to study biomolecular structures and their behavior in aqueous solution especially those of proteins, nucleic acids, carbohydrates, and viruses. The information obtained is in realistic conditions... 

The observed intensity of Raman scattering is proportional to the cross section, aj, with units of square centimeters per molecule. The magnitude of cry is related to 8a/8Qj, and significant theoretical treatment of this issue is available (1,4). One consequence of this theory is the variation of Raman... 

This article reviews all the published work concerned with the study of vibrational optical activity in chiral molecules from measurements of a small difference in the intensity of Raman scattering in right and left circularly polarized incident light. The history and basic theory are described briefly, followed by an account of the instrumentation and the precautions that must be observed in order to suppress spurious signals. The various theories that have been proposed in order to relate stereochemical features to the observations are then outlined, this being followed by a survey of all reported Raman optical activity spectra. 

The Raman approach to vibrational optical activity is based on measurement of a small difference in the intensity of Raman-scattered light from chiral molecules in right and left circularly polarized incident light, and several reviews have appeared previously1 -S). However, another review is now timely because important experimental and theoretical developments have since brought Raman optical activity (ROA) to a new level of maturity. 

Thus the condition for observation of Raman spectrum is a nonzero cf which is the selection rule. The intensity of Raman scattering, however depends on a number of factors, which includes the frequency of the scattered light (energy separation and hence populations), the density of vibrational states, the damping constant etc. In the case of glasses, an expression due to Shuker and Gammon (1971) for the Raman intensity of the Stokes lines is given by. 

Figure 5 15 Calculated values of the intensity of Raman scattering at various values of the scattering angle for m = ]. 5. The intensity is approximately proponional to the particle volume for. r > 2 (Stowers and Friedlander, 1998),...

The complete Stokes Raman spectrum covering shifts in the range 10-3500 cnr1 can be obtained and the intensity of Raman scattering is directly proportional to the concentration of the scattering species, an important factor for quantitative analysis. However, the Raman effect is relatively weak and hence a... 

The intensity of Raman scattering depends strongly on the excitation frequency.Figure 11 illustrates what happens if, for a given molecular system, we change excitation frequency so that it moves from the transparent region (a) to the... 

Figure 3.8. The time dependence of the intensities of Raman scattering for vibrational modes of trans-stilben. The figure insert displays a fitting. [Reprinted with permission from S. L. Schultz, J. Qian, and J. M. Jean, J. Phys. Chem., AlOl (1997), p. 1000. Copyright 1997, American Chemical Society.]...

The intensity of Raman scattering is proportional to the square of the change in the molecular polarizability a resulting from a normal mode q ... 

Fig. 8. Intensity of Raman scattering from a disc of miaxially oriented polymethylmethacrylate as a function of the orientation of the sample with respect to the polarisation vectors of the incident and scattered radiation. Results for the 604 cm line from a sample of birefringence /"nj —ri2 J (Reproduced by...

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