Cross Section resonant Raman

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... 

In resonance Raman experiments it is very important to consider the effect of the absorbed light on the sample composition. Raman scattering and absorption are independent events. Some photons are scattered, but a much larger number are absorbed. Cross sections for Raman scattering are on the order of 10" A /molecule, whereas cross sections for absorption are about 1 A /molecule. Thus, if photon absorption results in a photochemical transformation, as in the case of visual pigments, the effect of the photoalteration must be carefully considered. This situation has been analyzed in detail and rapid-flow methods devised that allow one to obtain resonance Raman spectra of even the most photolabile molecules without distortion of the sample composition. " ... 

A great disadvantage in any application of Raman spectroscopy is the extremely small cross-section of Raman scattering, between 10 and 10 cm /molecule. The larger value is obtained under resonance Raman conditions. With the discovery of a particular enhancement effect (upto 10 ) by Fleischmann et al. [2], that affects only species in close contact with the metal electrode surface and slightly later by Jeanmaire et al. [3] demonstrated surprisingly the feasibility of vibrational smdies of electrochemical interfaces with Raman spectroscopy... 

Resonant Excitation Excitation by a laser, which is resonant with an electronic transition of the material under investigation, can increase the Raman cross-section by approximately 10. The transitions and thus the resonance wavelengths are specific for the substances. Resonance excitation thus leads to selectivity that can be useful for suppressing bulk bands, but can also complicate the detection of mixtures of substance with different absorption spectra. 

A spontaneous Raman spectra is shown in Figure 2.8d in which the on- and off-resonant frequencies are indicated. The DNA bundles are observed at the resonant frequency, as shown in Figure 2.8a, while they cannot be seen at the off-resonant frequency in Figure 2.8b. This indicates that the observed contrast is dominated by the vibrationally resonant CARS signals. Figure 2.8c shows a cross-section of Figure 2.8a denoted by two solid arrows, which were acquired with a 5 nm step. The FWHM of... 

The TED and XRD patterns revealed that the deposit is not amorphous carbon but nanocrystalline diamond. Nonetheless, the 514-nm excited Raman spectra do not exhibit a clear diamond peak at 1332 cm though the peak due to the sp -bonded carbon network appears at 1150 cm The Raman cross section of the sp -bonded carbon network with visible excitation is resonantly enhanced [43, 48-50]. It consequently makes the 1332 cm diamond peak overlap with the peaks due to sp -bonded carbon. 

The hyperpolarizability tensor is obtained in a way similar to the case of SHG. However, the selection rules for an SFG resonance at the IR frequency implies that the vibrational mode is both IR and Raman active, as the SF hyperpolarizability tensor elements involve both an IR absorption and a Raman-anti-Stokes cross-section. Conversely, the DFG hyperpolarizability tensor elements involve an IR absorption and a Raman-Stokes cross-section. The hyperpolarizability tensor elements can be written in a rather compact form involving several vibrational excitations as [117] ... 

The key requirements for ISRS excitation are the existence of Raman active phonons in the crystal, and the pulse duration shorter than the phonon period loq1 [19]. The resulting nuclear oscillation follows a sine function of time (i.e., minimum amplitude at t=0), as shown in Fig. 2.2e. ISRS occurs both under nonresonant and resonant excitations. As the Raman scattering cross section is enhanced under resonant excitation, so is the amplitude of the ISRS-generated coherent phonons. 

Increasing the solvent polarity results in a red shift in the -t -amine exciplex fluorescence and a decrease in its lifetime and intensity (113), no fluorescence being detected in solvents more polar than tetrahydrofuran (e = 7.6). The decrease in fluorescence intensity is accompanied by ionic dissociation to yield the t-17 and the R3N" free radical ions (116) and proton transfer leading to product formation (see Section IV-B). The formation and decay of t-17 have been investigated by means of time resolved resonance Raman (TR ) spectroscopy (116). Both the TR spectrum and its excitation spectrum are similar to those obtained under steady state conditions. The initial yield of t-1 is dependent upon the amine structure due to competition between ionic dissociation and other radical ion pair processes (proton transfer, intersystem crossing, and quenching by ground state amine), which are dependent upon amine structure. However, the second order decay of t-1" is independent of amine structure... 

One simple explanation for these results was as follows The electric field at a metal vacuum interface can be >10 times larger than in free space when the conditions required for a surface plasma resonance are met (47). Since the Raman cross-section is proportional to the square of the field, surface plasmons could produce enhancements of >10. This enhancement is probably not large enough to explain the tunneling junction results by itself, but an enhancement in signal of a factor of 100 by the excitation of surface plasmons would increase the Raman intensity from near the limits of detectibility. 

Since most biomolecules normally exhibit medium or low Raman cross sections, an enhancement of the signal intensity for the ability to characterize even low concentrations would be preferable. Besides the application of resonance Raman spectroscopy, surface-enhanced Raman spectroscopy (SERS) is a promising alternative. In doing so the vicinity of molecules to rough noble metal surfaces leads to Raman enhancement factors of 106-108 and even up to 1014 leading to a single molecule detection limit [9]. 

Zhang, J.Z.H. and Miller, W.H. (1990). Photodissociation and continuum resonance Raman cross sections and general Franck-Condon intensities from 5-matrix Kohn scattering calculations with application to the photoelectron spectrum of H2F- + hv —> H2 + F, HF + H+e, J. Chem. Phys. 92, 1811-1818. 

M in concentration. This is in the range required for single-molecule detection. These sensitivity levels have been obtained on colloidal clusters at near-infrared excitation. Figure 10.3 is a schematic representation of a single-molecule experiment performed in a gold or silver colloidal solution. The analyte is provided as a solution at concentrations smaller than 10-11 M, Table 10.1 lists the anti-Stokes/Stokes intensity ratios for crystal violet (CY) at 1174 cm-1 using 830-nm near-infrared radiation well away from the resonance absorption of CY with a power of 106 W/cm2 [34]. CV is attached to various colloidal clusters as indicated in the table. Raman cross sections of 10-16 cm2/molecule or an enhancement factor of 1014 can be inferred from the data. 

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