Vibrational frequency shifts

Here te, tc are the correlation times of rotational and vibrational frequency shifts. The isotropic scattering spectrum corresponding to Eq. (3.15) is the Lorentzian line of width Acoi/2 = w0 + ydp- Its maximum is shifted from the vibrational transition frequency by the quantity coq due to the collapse of rotational structure and by the quantity A due to the displacement of the vibrational levels in a medium. 

It should be noted that there is a considerable difference between rotational structure narrowing caused by pressure and that caused by motional averaging of an adiabatically broadened spectrum [158, 159]. In the limiting case of fast motion, both of them are described by perturbation theory, thus, both widths in Eq. (3.16) and Eq (3.17) are expressed as a product of the frequency dispersion and the correlation time. However, the dispersion of the rotational structure (3.7) defined by intramolecular interaction is independent of the medium density, while the dispersion of the vibrational frequency shift (5 12) in (3.21) is linear in gas density. In principle, correlation times of the frequency modulation are also different. In the first case, it is the free rotation time te that is reduced as the medium density increases, and in the second case, it is the time of collision tc p/ v) that remains unchanged. As the density increases, the rotational contribution to the width decreases due to the reduction of t , while the vibrational contribution increases due to the dispersion growth. In nitrogen, they are of comparable magnitude after the initial (static) spectrum has become ten times narrower. At 77 K the rotational relaxation contribution is no less than 20% of the observed Q-branch width. If the rest of the contribution is entirely determined by... 

The ab initio SCF cluster wavefunction has been used to investigate the bonding of CO and CN- on Cu,0 (5,4,1), (5 surface layer, 4 second layer and 1 bottom layer atoms), and to calculate their field dependent vibrational frequency shifts in fields up to 5.2 x 107 V/cm(46). A schematic view of the Cu10 (5,4,l)CO cluster is shown in Figure 8. In order to assess the significance of Lambert s proposal, that the linear Stark effect is the dominant factor in the field dependent frequency shift, the effect of the field was calculated by three methods. One is by a fully variational approach (i.e., the adsorbate is allowed to relax under the influence of the applied field) in which the Hamiltonian for the cluster in a uniform electric field, F, is given by... 

Bigeleisen and Mayer (1947) simplified the reduced partition function by observing that vibrational frequency shifts caused by isotope substitution are relatively small (except when deuterium is substituted for normal hydrogen). When the dimensionless quantity hv/kr is of the order 5 or less (corresponding to a typical 1000 cm vibration at 288 K)—a condition applicable to most geochemical situations. 

A very interesting field of research covers the spectroscopy of van der Waals molecules in search of more detailed information about the long range potential and the polarizability. Raman spectra of van der Waals dimers in argon have been observed and a vibrational frequency shift for I2-molecules from 213 cm" to 197 cm has been measured for I2 -Ar-complexes. 

The ratio of symmetry numbers s s° in equation 11.40 merely represents the relative probabilities of forming symmetrical and unsymmetrical molecules, and ni and nf are the masses of exchanging molecules (the translational contribution to the partition function ratio is at all T equal to the power ratio of the inverse molecular weight). Denoting as AX, the vibrational frequency shift from isotopically heavy to light molecules (i.e., AX, = X° — X ) and assuming AX, to be intrinsically positive, equation 11.40 can be transated into... 

For future experimental comparisons, we calculated a vibrational frequency shift for the hydrogen molecule moieties of 216cm TZ 2>d f, p) CCSD(T), scaled by 0.95] relative to free hydrogen (Table 13). This frequency corresponds to the asymmetric H-4I stretching mode because the symmetric motion has zero oscillator... 

In order to derive a practical approximation for the repulsive contribution to vibrational frequency shifts the excess chemical potential, A ig, associated with the formation of a hard diatomic of bond length r from two hard spheres at infinite separation in a hard sphere reference fluid is assumed to have the following form. 

This perturbative expression for the attractive force shift is derived from a van der Waals mean field approximation (23). Although the predictions of this model have been found to agree with numerous high pressure vibrational frequency shift measurements (23,25,28), a non-linear attractive force model has recently been suggested to be appropriate for some systems (26,27). 

Figure 4. Vibrational frequency shifts as a function of density in supercritical fluid nitrogen and methane. The experimental and theoretical shifts are measured relative to their zero density vapor phase values (see table I).

The hard fluid model is found to quantitatively reproduce observed vibrational frequency shifts in supercritical N2, CH4 and near critical C2H5. In nitrogen and methane at room temperature T/Tc is equal to 2.3 and 1.5, respectively. At such high reduced temperatures repulsive forces are expected to exert a predominant influence on fluid structure. Thus it is perhaps not surprising that the hard fluid model is successful in reproducing the observed frequency shifts in these two fluids. 

Our vibrational frequency shift measurements in pure SCF systems can be viewed... 

Vibrational frequency shift, relative to low density vapor... 

J. Wang, R. J. Boyd, and A. Laaksonen, J. Cbem. Pbys., 104, 7261. A Hybrid Quantum Mechanical Force Field Molecular Dynamics Simulation of Liquid Methanol Vibrational Frequency Shifts as a Probe of the Quantum Mechanical/Molecular Mechanical Coupling. 

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

C. M. Morales and W. H. Thompson. Mixed quantum-classical molecular dynamics analysis of the molecular-level mechanisms of vibrational frequency shifts. J.Phys. Chem. A, lll(25) 5422-5433, JUN 28 2007. 

The recent progress of computational quantum chemistry has made it possible to get realistic descriptions of vibrational frequencies for polyatomic molecules in solution. The first attempt in this direction was made by Rivail el al. [1] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium to compute vibrational frequency shifts for molecular solutes. An extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [2 1] in the framework of the Polarizable Continuum Model (PCM). 

More recently, the PCM has been amply extended to the treatment of vibrational spectroscopies, by taking into account not only solvent-induced vibrational frequency shifts, but also vibrational intensities in a unified and coherent formulation. Thus, models to treat IR [8], Raman [9], IR linear dichroism [10], VCD [11] and VROA [12] have been proposed and tested, by including in the formulation local field effects, as well as an incomplete solute-solvent regime (nonequilibrium) and, when necessary, by extending the model to the treatment of specific solute-solvent (or solute-solute) effects. 

The TCNQ- radical thus obtained is completely stable for at least 3 hr, and its electronic spectrum shows strong absorption bands between 950 and 550 nm. Thus, the RR spectrum of TCNQ-- was obtained by using the 647.1 nm line of a Kr+ laser (Fig. 3-20a). On the other hand, TCNQ has a strong absorption band near 400 nm. Therefore, its preresonance spectrum, shown in Fig. 3-20b, was obtained by the 457.9 nm line of an Ar+ laser. In both spectra, all strong and medium intensity bands were found to be polarized (totally symmetric). The vibrational frequency shifts in going from... 

Fe with the template ion. DTA studies indicate that Fe-faujasites have lower thermal stability than their Al—analogs.The (OH) vibration frequency shifts from 3540 and 3630 to 3570 and 3643 cm respectively on isomorphous substitution of Al by Fe. Relative changes in the intensity of the ESR peak at g = 4.3 at low temperatures also support the conclusion that iron can be inserted in the fauja-site lattice positions. 

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