Resonance Raman cross-section

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. 

Quantum mechanically, resonance Raman cross-sections can be calculated by the following sum-over-states expression derived from second-order perturbation theory within the adiabatic, Born-Oppenheimer and harmonic approximations... 

Within the separable harmonic approximation, the < f i(t) > and < i i(t) > overlaps are dependent on the semi-classical force the molecule experiences along this vibrational normal mode coordinate in the excited electronic state, i.e. the slope of the excited electronic state potential energy surface along this vibrational normal mode coordinate. Thus, the resonance Raman and absorption cross-sections depend directly on the excited-state structural dynamics, but in different ways mathematically. It is this complementarity that allows us to extract the structural dynamics from a quantitative measure of the absorption spectrum and resonance Raman cross-sections. 

The resonance Raman cross-section, ctr, can be measured experimentally from the resonance Raman intensity by the following equation... 

Besides the sum-over-states and time-dependent models for the resonance Raman cross-section, other models can be used to calculate resonance Raman cross-sections, such as the transform and time correlator models. In the transform model, the resonance Raman cross-sections as a function of excitation energy, the excitation profiles, can be calculated from the absorption spectrum within the separable harmonic oscillator approximation directly by the following relationship [85-87]... 

The time correlator method [85, 88, 89] has not been used as frequently as the other methods described here, and has not been used for nucleic acids and their components. It will therefore not be discussed further. The experimental methods for determining absolute Raman and resonance Raman cross-sections have been extensively reviewed [90-93], Similarly, the methods for practical use of the sum-over-states, time-dependent, and transform methods for determining excited-state structural dynamics have been extensively reviewed [78-83],... 

The UV resonance Raman spectrum of thymine was revisited in 2007, with a slightly different approach, by Yarasi, et al. [119]. Here, the absolute UV resonance Raman cross-sections of thymine were measured and the time-dependent theory was used to experimentally determine the excited-state structural dynamics of thymine. The results indicated that the initial excited-state structural dynamics of thymine occurred along vibrational modes that are coincident with those expected from the observed photochemistry. The similarity in a DFT calculation of the photodimer transition state structure [29] with that predicted from the UV resonance Raman cross-sections demonstrates that combining experimental and computational techniques can be a powerful approach in elucidating the total excited-state dynamics, electronic and vibrational, of complex systems. 

What is remarkable is that all of these early measurements of the UV resonance Raman spectra of nucleic acid components involved computational and theoretical support to their experimental findings. For example, Spiro used CINDO calculations to determine the nature of the excited electronic states of the nucleotides [157], In the early and mid 1970 s, many researchers were also attempting to understand resonance Raman spectroscopy, the types of information it could provide, and a unifying theoretical framework to the intensities [147, 159-172], UV resonance Raman spectra provided some of the first experimental evidence to test the various theoretical models. Peticolas attempted to fit the observed experimental excitation profiles of AMP [156], UMP [151, 154] and CMP [152, 153] to the sum-over-states model for the resonance Raman cross-sections. From these simulations, they were able to obtain preliminary excited-state structural dynamics of the nucleobase chromophores of the nucleotides for UMP [151, 153, 158] and CMP [153], For AMP, the experimental excitation profiles were simulated with an A-term expression, but the excited-state structural changes were not obtained. Rather, the goal of that work was to identify the electronic transitions within the lowest-energy absorption band of adenine [156],... 

Meyer. S.A.. Le Ru. E.C.. and Etchegoin, P.G. (2010) Quantifying resonant Raman cross sections with SERS. 

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. 

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. 

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]. 

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. 

Catalytic reaction conditions or the exposure to reducing environments may lead to the formation of reduced surface metal oxide species. It is generally difficult to obtain good Raman signals for reduced supported metal oxide species because of their low Raman cross-sections. On the other hand, many reduced transition metal ions have electronic absorption bands in the visible regime. Hence, the laser frequency may be tuned to these absorption bands, and resonantly enhanced Raman spectra should be obtained. 

Resonance Raman and NMR Studies. The major support to the protonation hypothesis is presently based on the recent application of resonance-Raman spectroscopy. (For recent reviews, see refs. 217-219.) The method uses an incident beam which is in resonance with the absorption of the retinyl chromophore. This results in the selective enhancement of the Raman cross sections coupled with the chromophore, relative to the very weak, non-resonant, modes of the opsin. Characteristic spectra are shown in Fig. 6. Early evidence for protonation came from the observation of a close similarity between the C=N vibrational frequency in rhodopsin and in a model protonated Schiff base (220). More conclusive arguments were provided by Oseroff and Callender, who carried out experiments at low temperatures in order to control sample photoability (221). It was observed that deuteration shifts the C=N vibration frequency from 1655 cm- to 1630 cm-- -, both in the pigment and in a model protonated Schiff base. 

The molecular cross section of the ordinary Raman effect can be considerably enhanced. If the exciting radiation has a higher frequency, the intensity increases basically by the fourth power of the frequency. Moreover, there is a further increase as electronic absorption bands are approached the pre-resonance and resonance Raman effect (Sections 3.6 and 6.1). Further, the so-called surface-enhanced Raman effect (SERS) increases the molecular cross section. Both effects produce an enhancement of several orders of magnitude (Gerrard, 1991) (see Sec. 6.1). However, these two effects have to be carefully adapted to the specific properties of the investigated molecules. Photochemical decomposition and excitation of fluorescence may make it impossible to record a Raman spectrum. The described techniques may thus be of considerable importance for the solution of special problems, but they are by no means routine techniques to be generally used. 

Although nothing can be done to make the Raman cross-section of vibrational bands any greater without the application of techniques such as resonance Raman spectroscopy or surface-enhanced Raman scattering, several important technological developments have led to the design of today s truly powerful Raman spectrometers. These included (in no particular historical order) the development of... 

Resonance Raman spectroscopy has been discussed by many authors [4, 5, 6, 7, 8, 9,10,11,12,13,14 and 15]. If the excitation frequency is resonant with an excited electronic state, it is possible to dramatically increase the Raman cross-section. It is still a scattering process without absorption, but the light and... 

---