Functional Raman

Keywords Single-wall carbon nanotube, noncovalent nanotube functionalization, Raman... 

Small-angle X-ray scattering (SAXS) Powder diffraction Eiber diffraction Hermann s orientation function Raman spectroscopy... 

Infrared and Raman spectroscopy each probe vibrational motion, but respond to a different manifestation of it. Infrared spectroscopy is sensitive to a change in the dipole moment as a function of the vibrational motion, whereas Raman spectroscopy probes the change in polarizability as the molecule undergoes vibrations. Resonance Raman spectroscopy also couples to excited electronic states, and can yield fiirtlier infomiation regarding the identity of the vibration. Raman and IR spectroscopy are often complementary, both in the type of systems tliat can be studied, as well as the infomiation obtained. 

Joe T and Albrecht A C 1993 Femtosecond time-resolved coherent anti-Stokes Raman spectroscopy of liquid benzene a Kubo relaxation function analysis J. Chem. Phys. 99 3244-51... 

In an ambitious study, the AIMS method was used to calculate the absorption and resonance Raman spectra of ethylene [221]. In this, sets starting with 10 functions were calculated. To cope with the huge resources required for these calculations the code was parallelized. The spectra, obtained from the autocorrelation function, compare well with the experimental ones. It was also found that the non-adiabatic processes described above do not influence the spectra, as their profiles are formed in the time before the packet reaches the intersection, that is, the observed dynamic is dominated by the torsional motion. Calculations using the Condon approximation were also compared to calculations implicitly including the transition dipole, and little difference was seen. 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

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. 

Selected physical properties are given ia Table 4. The nmr data (97) and ir and Raman spectra (98) have also been determined. Thermodynamic functions have been calculated from spectral data (99). 

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

The ease of sample handling makes Raman spectroscopy increasingly preferred. Like infrared spectroscopy, Raman scattering can be used to identify functional groups commonly found in polymers, including aromaticity, double bonds, and C bond H stretches. More commonly, the Raman spectmm is used to characterize the degree of crystallinity or the orientation of the polymer chains in such stmctures as tubes, fibers (qv), sheets, powders, and films... 

Figure 1 indicates how the NO concentrations vary at 20°C as a function of the molar composition of the acid mixture these results were determined using Raman spectra readings. 

Normal mode analysis exists as one of the two main simulation techniques used to probe the large-scale internal dynamics of biological molecules. It has a direct connection to the experimental techniques of infrared and Raman spectroscopy, and the process of comparing these experimental results with the results of normal mode analysis continues. However, these experimental techniques are not yet able to access directly the lowest frequency modes of motion that are thought to relate to the functional motions in proteins or other large biological molecules. It is these modes, with frequencies of the order of 1 cm , that mainly concern this chapter. 

Because Raman spectroscopy requires one only to guide a laser beam to the sample and extract a scattered beam, the technique is easily adaptable to measurements as a function of temperature and pressure. High temperatures can be achieved by using a small furnace built into the sample compartment. Low temperatures, easily to 78 K (liquid nitrogen) and with some diflSculty to 4.2 K (liquid helium), can be achieved with various commercially available cryostats. Chambers suitable for Raman spectroscopy to pressures of a few hundred MPa can be constructed using sapphire windows for the laser and scattered beams. However, Raman spectroscopy is the characterizadon tool of choice in diamond-anvil high-pressure cells, which produce pressures well in excess of 100 GPa. ... 

Some materials undergo transitions from one crystal structure to another as a function of temperature and pressure. Sets of Raman spectra, collected at various temperatures or pressures through the transition often provide useftil information on the mechanism of the phase change first or second order, order/disorder, soft mode, etc. 

Determination of surface functional groups, e.g., —OH, —C - C—, and >C = O, and identificadon of adsorbed molecules comes principally from comparison with vibrational spectra (infixed and Raman) of known molecules and compounds. Quick qualitative analysis is possible, e.g., stretching modes involving H appear for v(C—H) at 3000 cm and for v(0—H) at 3400 cm L In addition, the vibrational energy indicates the chemical state of the atoms involved, e.g., v(C=C) " 1500 cmT and v(C=0) " 1800 cm"L Further details concerning the structure of adsorbates... 

State or vibrational energies. If the current across the metal-insulator-metal sandwich is recorded as a function of applied voltage, the current increases as the threshold for each state or vibrational mode is crossed. The increases in current are in fact very small, and for improved detectability the current is double-differentiated with respect to voltage, thereby providing, in effect, a vibrational spectrum that can be compared directly with free-molecule IR and Raman spectra. 

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). 

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].

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