Vibration-rotation band shapes

Before discussing vibration-rotation band shapes, it is appropriate to consider "pure rotational" Raman spectra in dense fluids (often called inelastic light scattering). The argument closely parallels that for i.r. absorption, but with the added complication of polarized and depolarized scattering. In the depolarized case, one has a "self" term which is ... 

Infrared absorption properties of 2-aminothiazole were reported with those of 52 other thiazoles (113). N-Deuterated 2-aminothiazole and 2-amino-4-methylthiazo e were submitted to intensive infrared investigations. All the assignments were performed using gas-phase studies of the shape of the vibration-rotation bands, dichroism, isotopic substitution, and separation of frequencies related to H-bonded and free species (115). With its ten atoms, this compound has 24 fundamental vibrations 18 for the skeleton and 6 for NHo. For the skeleton (Cj symmetry) 13 in-plane vibrations of A symmetry (2v(- h, 26c-h- Irc-N- and 7o)r .cieu.J and... 

The shape of the vibration-rotation bands in infrared absorption and Raman scattering experiments on diatomic molecules dissolved in a host fluid have been used to determine2,15 the autocorrelation functions unit vector pointing along the molecular axis and P2(x) is the Legendre polynomial of index 2. These correlation functions measure the rate of rotational reorientation of the molecule in the host fluid. The observed temperature- and density-dependence of these functions yields a great deal of information about reorientation in solids, liquids, and gases. These correlation functions have been successfully evaluated on the basis of molecular models.15... 

Electronic spectra are almost always treated within the framework of the Bom-Oppenlieimer approxunation [8] which states that the total wavefiinction of a molecule can be expressed as a product of electronic, vibrational, and rotational wavefiinctions (plus, of course, the translation of the centre of mass which can always be treated separately from the internal coordinates). The physical reason for the separation is that the nuclei are much heavier than the electrons and move much more slowly, so the electron cloud nonnally follows the instantaneous position of the nuclei quite well. The integral of equation (BE 1.1) is over all internal coordinates, both electronic and nuclear. Integration over the rotational wavefiinctions gives rotational selection rules which detemiine the fine structure and band shapes of electronic transitions in gaseous molecules. Rotational selection rules will be discussed below. For molecules in condensed phases the rotational motion is suppressed and replaced by oscillatory and diflfiisional motions. 

Infrared spectroscopy has broad appHcations for sensitive molecular speciation. Infrared frequencies depend on the masses of the atoms iavolved ia the various vibrational motions, and on the force constants and geometry of the bonds connecting them band shapes are determined by the rotational stmcture and hence by the molecular symmetry and moments of iaertia. The rovibrational spectmm of a gas thus provides direct molecular stmctural information, resulting ia very high specificity. The vibrational spectmm of any molecule is unique, except for those of optical isomers. Every molecule, except homonuclear diatomics such as O2, N2, and the halogens, has at least one vibrational absorption ia the iafrared. Several texts treat iafrared iastmmentation and techniques (22,36—38) and thek appHcations (39—42). 

Y most probably has coexisting nuclear shapes with a well developed rotational band on the 495 keV level and other levels which seem to be rather of vibrational nature. 

The allowed changes in the rotational quantum number J are AJ = 1 for parallel (2 ) transitions and A7= 0, 1 for perpendicular (II ) transitions. Parallel transitions such as for acetylene thus have P i J= 1) and R(AJ = +1) branches with a characteristic minimum between them, as shown for diatomic molecules such as HCl in Fig. 37-3 and for the HCN mode in Fig. 2. However, perpendicular transitions such as Vs for acetylene and V2 for HCN (Fig. 2) have a strong central Q branch (AJ = 0) along with P and R branches. This characteristic PQR-Yersus-PR band shape is quite obvious in the spectrum and is a useful aid in assigning the symmetries of the vibrational levels involved in the infrared transitions of a hnear molecule. 

Temperature information from CARS spectra derives from spectral shapes either of the 2-branches or of the pure rotational CARS spectra of the molecular constituents. In combustion research it is most common to perform thermometry from nitrogen since it is the dominant constituent and present everywhere in large concentration despite the extent of chemical reaction. The 2-branch of nitrogen changes its shape due to the increased contribution of higher rotational levels which become more populated when the temperature increases. Figure 6.1-21 displays a calculated temperature dependence of the N2 CARS spectrum for experimental parameters typically used in CARS thermometry (Hall and Eckbreth, 1984). Note that the wavenumber scale corresponds to the absolute wavenumber value for the 2320 cm 2-branch of N2 when excited with the frequency doubled Nd.YAG laser at 532 nm ( 18796 cm ), i. e. = 18796 -1- 2320 = 21116 cm. The bands lower than about 21100 cm are due to the rotational structure of the first vibrational hot band. 

Although translational and rotational contributions to the vibrational density of states can be calculated using rigid molecule potentials, relatively little has been done using such models. Rather, flexible molecule potentials have been used, in which case the band shapes and their frequency ranges can be computed for all three types of vibration. Most calculations to date have used either completely classical studies or introduced quantum effects in an approximate way. We will give an overview of both approaches. 

E.E.Nikitin, Band shapes of pressure-induced vibrational and rotational spectra of diatomic molecules, Optika i Spektr. 7, 744 (1959)... 

E.E.Nikitin, Band shapes of induced rotational and vibrational spectra of diatomic molecules, in Adv. Molec. Spectroscopy, Pergamon Press, p.298 (1962) E.E.Nikitin, Resonance and nonresonance intermoleeular energy exchange in molecular collisions, Disc.Faraday Soc. 33, 14 (1962)... 

Experimental data pertinent to the vibrational predisaociation mechanism of two types of van der Waals complex are presented and discussed. First, variations in the infrared band shape for excitation of the ethylene out-of-plane wag, Vy, in the series of molecules CjH tHF, C2H Ne are discussed in terms of structure and relaxation mechanisms. Second, rotationally resolved laser excited fluorescence spectra for NeBr2 and NeCl2 are presented. There is a strong dependence of decay rate on molecular structure.. Relaxation... 

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