Intensities Raman

SERS. A phenomenon that certainly involves the adsorbent-adsorbate interaction is that of surface-enhanced resonance Raman spectroscopy, or SERS. The basic observation is that for pyridine adsorbed on surface-roughened silver, there is an amazing enhancement of the resonance Raman intensity (see Refs. 124—128). More recent work has involved other adsorbates and colloidal... 

Myers A B and Mathies R A 1987 Resonance Raman intensities A probe of excited-state structure and dynamics Biological Applications of Raman Spectroscopy yo 2, ed T G Spiro (New York Wiley-Interscience) pp 1-58... 

The siim-over-states method for calculating the resonant enlrancement begins with an expression for the resonance Raman intensity, /.y, for the transition from initial state to final state /in the ground electronic state, and is given by [14]... 

It is also possible to detennine the resonant Raman intensities via a time-dependent method [16]. It has the... 

Shreve A P and Mathies R A 1995 Thermal effects in resonance Raman-scattering—analysis of the Raman intensities of rhodopsin and of the time-resolved Raman-scattering of bacteriorhodopsin J. Phys. Chem. 99 7285-99... 

Tang J and Albrecht A C 1970 Developments in the theories of vibrational Raman intensities Raman Spectroscopy Theory and Practice vol 2, ed H A Szymanski (New York Plenum) pp 33-68... 

The Franck-Condon principle reflected in tire connection between optical and tliennal ET also relates to tire participation of high-frequency vibrational degrees of freedom. Charge transfer and resonance Raman intensity bandshape analysis has been used to detennine effective vibrational and solvation parameters [42,43]. 

The intensities are plotted vs. v, the final vibrational quantum number of the transition. The CSP results (which for this property are almost identical with CI-CSP) are compared with experimental results for h in a low-temperature Ar matrix. The agreement is excellent. Also shown is the comparison with gas-phase, isolated I. The solvent effect on the Raman intensities is clearly very large and qualitative. These show that CSP calculations for short timescales can be extremely useful, although for later times the method breaks down, and CTCSP should be used. 

A number of molecular properties can be computed. These include ESR and NMR simulations. Hyperpolarizabilities and Raman intensities are computed using the TDDFT method. The population analysis algorithm breaks down the wave function by molecular fragments. IR intensities can be computed along with frequency calculations. 

Q-Chem includes HF, ROHF, UHF, and MP2 Hamiltonians as well as a good selection of DFT functionals. Mulliken and NBO population analysis methods are available. Multiple options are available for SCF convergence, geometry optimization, and initial guess. IR and Raman intensities can also be computed. In addition, the documentation was well written. 

Figure 6.2 shows typically how a varies with r da/dr is usually positive and, unlike d/r/dr in Figure 6.1, varies little with r. For this reason vibrational Raman intensities are less sensitive than are infrared intensities to the environment of the molecule, such as the solvent in a solution specttum. 

Large Specific Surface Area Porous materials can have a large proportion of surface atoms - their surface area within a typical sampling volume of 10 pm can reach 10 pm, which is approximately 10 larger than for a smooth surface crossing the same volume. These effects lead to clearly increased Raman intensities of surface species and also to improved intensity ratios of surface and bulk Raman bands. 

Surface-enhancement Electromagnetic and chemical effects can enhance the Raman intensities from substances in close proximity to appropriate metal surfaces by several orders of magnitude. 

In Raman spectroscopy the intensity of scattered radiation depends not only on the polarizability and concentration of the analyte molecules, but also on the optical properties of the sample and the adjustment of the instrument. Absolute Raman intensities are not, therefore, inherently a very accurate measure of concentration. These intensities are, of course, useful for quantification under well-defined experimental conditions and for well characterized samples otherwise relative intensities should be used instead. Raman bands of the major component, the solvent, or another component of known concentration can be used as internal standards. For isotropic phases, intensity ratios of Raman bands of the analyte and the reference compound depend linearly on the concentration ratio over a wide concentration range and are, therefore, very well-suited for quantification. Changes of temperature and the refractive index of the sample can, however, influence Raman intensities, and the band positions can be shifted by different solvation at higher concentrations or... 

Quantification at surfaces is more difficult, because the Raman intensities depend not only on the surface concentration but also on the orientation of the Raman scat-terers and the, usually unknown, refractive index of the surface layer. If noticeable changes of orientation and refractive index can be excluded, the Raman intensities are roughly proportional to the surface concentration, and intensity ratios with a reference substance at the surface give quite accurate concentration data. 

Fig. 4.60. Comparison of resonance Raman spectra with and without tip enhancement for 0.5 monolayers of brilliant cresyl blue on a smooth gold film. The tip increased the total Raman intensity by a factor of approximately 15, when positioned at a tunneling distance of 1 nm. Several other bands were made visible as a result of the tip enhancement [4.306].

An interesting point concerns polarisation effects in the Raman spectra, which are commonly observed in low-dimensional materials. Since CNTs are onedimensional (ID) materials, the use of light polarised parallel or perpendicular to the tube axis will give information about the low dimensionality of the CNTs. The availability of purified samples of aligned CNTs would allow us to obtain the symmetry of a mode directly from the measured Raman intensity by changing the experimental geometry, such as the polarisation of the light and the sample orientation, as discussed in this chapter. 

In the following sections, we first show the phonon dispersion relation of CNTs, and then the calculated results for the Raman intensity of a CNT are shown as a function of the polarisation direction. We also show the Raman calculation for a finite length of CNT, which is relevant to the intermediate frequency region. The enhancement of the Raman intensity is observed as a function of laser frequency when the laser excitation frequency is close to a frequency of high optical absorption, and this effect is called the resonant Raman effect. The observed Raman spectra of SWCNTs show resonant-Raman effects [5, 8], which will be given in the last section. 

Using the calculated phonon modes of a SWCNT, the Raman intensities of the modes are calculated within the non-resonant bond polarisation theory, in which empirical bond polarisation parameters are used [18]. The bond parameters that we used in this chapter are an - aj = 0.04 A, aji + 2a = 4.7 A and an - a = 4.0 A, where a and a are the polarisability parameters and their derivatives with respect to bond length, respectively [12]. The Raman intensities for the various Raman-active modes in CNTs are calculated at a phonon temperature of 300K which appears in the formula for the Bose distribution function for phonons. The eigenfunctions for the various vibrational modes are calculated numerically at the T point k=Q). 

When we compare the VV with the VH configurations for the polarised light, the Raman intensity shows anisotropic behaviour. Most importantly, the A g mode at 165 cm is suppressed in the VH configuration, while the lower frequeney E g and E2g modes are not suppressed. This anisotropy is due to the... 

Fig. 3. Raman intensities as a function of the sample orientation for the (10, 10) armchair CNT. As shown on the right, 0 and 62 are angles of the CNT axis from the z axis to the x axis and the y axis, respectively. 63 is the angle of the CNT axis around the z axis from the x axis to the y axis. The left and right hand figures correspond to the VV and VH polarisations [12].

When we compare the calculated Raman intensities for armchair, zigzag and chiral CNTs of similar diameters, we do not see large differences in the lower frequency Raman modes. This is because the lower frequency modes have a long... 

Raman modes. Such a symmetry analysis will also be useful for identifying the chirality of CNTs. The spectral features in the intermediate frequency range may come from the finite length of CNTs. The resonant Raman intensity may reflect differences in the DOS between metallic and semiconducting CNTs. 

Figure 5. (a) The ( A, SO,) anion symmetric streching mode of polypropylene glycol)- LiCF,SO, for 0 M ratios of 2000 1 and 6 1. Solid symbols represent experimental data after subtraction of the spectrum corre-ponding to the pure polymer. Solid curves represent a three-component fit. Broken curves represent the individual fitted components, (b) Relative Raman intensities of the fitted profiles for the ( Aj, SO,) anion mode for this system, plotted against square root of the salt concentration, solvated ions ion pairs , triple ions, (c) The molar conductivity of the same system at 293 K. Adapted from A. Ferry, P. Jacobsson, L. M. Torell, Electrnchim. Acta 1995, 40, 2369 and F. M. Gray, Solid State Ionics 1990, 40/41, 637. 

Since Raman scattered light intensity is very weak, of the order of 10-7 of the excitation line intensity, more powerful laser sources than the He-Ne laser are often needed. The Ar+ laser emits various lines in the region from 457.9 nm to 514.5 nm, of which the most powerful lines (typically — 700 mW) at 488.0 nm (blue) and 514.5 nm (green) are preferred. Furthermore, two other factors which favor the use of the high frequency excitation lines are the peak sensitivity of the photomultipliers in this blue-green region (Fig. 8) and the fourth power Raman intensity law... 

Table 1 Harmonic fundamental modes of the three most stable isomers of S4 with infrared and Raman intensities calculated at the B3LYP/6-31G(2df) level of theory [9]. Symmetrical modes (of symmetry A) are shown in italics. For the connectivities of the S4 isomers, see Scheme 1. Experimental wavenumbers are given for comparison assignments according to [9] using experimental data from [17, 76] ...

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