Raman spectroscopy quantum model

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

At higher pressures only Raman spectroscopy data are available. Because the rotational structure is smoothed, either quantum theory or classical theory may be used. At a mixture pressure above 10 atm the spectra of CO and N2 obtained in [230] were well described classically (Fig. 5.11). For the lowest densities (10-15 amagat) the band contours have a characteristic asymmetric shape. The asymmetry disappears at higher pressures when the contour is sufficiently narrowed. The decrease of width with 1/tj measured in [230] by NMR is closer to the strong collision model in the case of CO and to the weak collision model in the case of N2. This conclusion was confirmed in [215] by presenting the results in universal coordinates of Fig. 5.12. It is also seen that both systems are still far away from the fast modulation (perturbation theory) limit where the upper and lower borders established by alternative models merge into a universal curve independent of collision strength. 

In the main text we arrive at the same conclusion regarding the possible frequency shifts based on a qualitative discussion of vibronic states. The complete quantum model of Raman spectroscopy also has to take into account the change of polarizability accompanying the transition between stationary vibrational states, which leads to the coupling factor in Equation (6.15). 

The combination of classical electrochemical measurements with ex situ transfer experiments into UHV [242], and in situ structure-sensitive studies such as electroreflectance [25], Raman and infrared (IR)-spectroscopies [29, 243], and more recently STM and SXS [39] provided detailed knowledge on energetic, electronic and structural aspects of (ordered) anion adsorption and phase formation. These experimental studies have been complemented by various theoretical approaches (1) quantum model calculations to explore substrate-adsorbate interactions [244-246] (2) computer simulation techniques to analyze the ion and solvent distribution near the interface [247] (3) statistical models [67] and (4) MC simulations [38] to describe phase transitions in anionic adlayers. 

Raman spectra - like IR spectra - include detailed information about the molecular structure and, hence, may provide a key for elucidating structure-function relationships. Unfortunately, the ability to extract structural data from the spectra is much less advanced than, for example, in NMR spectroscopy, since a sound vibrational analysis based on normal mode calculations is not straightforward. Empirical force fields only provide meaningful results in the case of small and/or symmetric molecules for which a large set of isotopomers are available. Alternatively, quantum chemical methods can be employed to calculate the force constants. Despite the recent progress in hard- and software development, this approach is as yet restricted to prosthetic groups and building blocks of biopolymers. Thus, in most cases the interpretation of the Raman spectra of biomolecules is based on empirical relationships derived from comparative studies of model compounds. 

Several methodologies based on potentiometric titrations, microelectrophoresis and macroscopic adsorption measnrements have been used in conjunction with Diffuse Reflectance, Raman and Electron Paramagnetic Resonance spectroscopy. Semi-empirical qnantum mechanical calculations, stereochemical considerations and quantum mechanical calculations in the frame of the DFT are followed. The above are then used for developing a quantitative model for the interfacial deposition studied. Details concerning the combined application of these methodologies to obtain the interfacial stmctnre and speciation of the aforementioned species have been reported elsewhere [4-10]. The majority crystal terminations (1 0 1) and (1 0 0) of the anatase nanociystals, comprised in the titania grains, were chosen to exemplify the interfacial stmctures. A titania rich in anatase (Degussa P25) has been used in all cases. 

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