Qualitative motional description

The shift in the two tensors is expected to be effective for carbohydrate molecules bearing a number of polar groups and hydrogen-bonding centers. Hence, serious difficulty for quantitative analysis may arise if the molecule does not contain three or more nonequivalent C—H vectors that relax predominantly via the overall motion. If this fact is ignored, qualitative treatment may lead to an erroneous motional description. Thus, one should be very cautious in interpreting the relaxation data for overall motion, especially when discrepancies well outside the experimental error are observed for the T, values. When the relaxation times are nearly similar and within the experimental error, isotropic motion may be considered as a first approximation to the problem. 

Table I, which lists a number of mono-, oligo-, and polysaccharides and derivatives whose motional descriptions are available based on qualitative arguments, summarizes the experimental conditions and types of measurements used to obtain those descriptions. Table II deals specifically with those carbohydrates for which a quantitative treatment and dynamic modeling have been undertaken. In naming the compounds listed in Tables I and II, IUPAC rules are used for monosaccharide and less complex oligosaccharide molecules. However, empirical names are used for unusual oligosaccharides involving a complex aglycon substituent and polysaccharides. The gross motional features of a number of the compounds in Table I have been discussed in references 6-8, and will be mentioned here only if necessary for further clarification or for comparison with quantitative results.

It should be emphasized that many constitutive models have been proposed especially for polymeric solutions and melts, and there is a great deal of current research that is aimed at both new models25 and numerical analysis of fluid motions by use of the existing models 26 The problem is that few have been carefully compared with the behavior of real fluids outside the highly simplistic flows of conventional rheometers, and then mainly under flow conditions in which the perturbations in material structure are weak. Thus there is currently no model that is known to provide quantitatively accurate or even qualitatively reliable descriptions of real complex fluids for a wide spectrum of flows. 

Both infrared and Raman spectroscopy provide infonnation on the vibrational motion of molecules. The teclmiques employed differ, but the underlying molecular motion is the same. A qualitative description of IR and Raman spectroscopies is first presented. Then a slightly more rigorous development will be described. For both IR and Raman spectroscopy, the fiindamental interaction is between a dipole moment and an electromagnetic field. Ultimately, the two... 

We can be qualitatively certain that the fluidlike flow of shock deformation is a consequence of motion of defects. We cannot be quantitatively certain as to the significant, detailed descriptions and consequences of these defects. Indeed, the principal unfinished business of shock-compression science is the scientific description of the defective solid in all its manifestations. 

From this brief description it is quite apparent that the qualitative elements of the Marcus treatment for an electron transfer process are identical to the CM model. In CM terms the reaction involves the avoided crossing of reactant (Fe2+ + Fe3+) with product (Fe3+ + Fe2+) configurations, with the reaction co-ordinate just being the distortion-relaxation motion of the solvation sphere. Thus in CM terms any electron transfer reaction involves the avoided crossing of the DA (donor-acceptor) and D+A" configurations, and for such reactions at least, based on the equivalence with Marcus theory, the CM model has a solid foundation. 

The torsional motion of biphenyl and related compounds is a typical large amplitude motion. The accumulated knowledge from a series of molecules in this group has led to a fairly good qualitative description of the motion. Unfortunately the quantitative description leaves much to be desired. Taking advantage of the improvements in the electron-diffraction method and applying suitable combinations with other methods, there are reasons to believe that this deficiency should be remedied. 

In our early work33 [50] the constant field model was applied to liquid water, where the harmonic law of particles motion, corresponding to a parabolic potential, was actually employed in the final calculations of the complex permittivity. In this work, qualitative description of only the libration band was obtained, while neither the R-band nor the low-frequency (Debye) relaxation band was described. Moreover, the fitted mean lifetime x of the dipoles, moving in the potential well, is unreasonably short ( ().02 ps)—that is, about an order of magnitude less than in more accurate calculations, which will be made here. 

In the first place, the averaged model equations are highly nonlinear and require sophisticated numerical analysis for solution. For example, the attempt to obtain numerical solutions for motions of polymeric liquids, based upon simple continuum, constitutive equations, is still not entirely successful after more than 10 years of intensive effort by a number of research groups worldwide [27]. It is possible, and one may certainly hope, that model equations derived from a sound description of the underlying microscale physics will behave better mathematically and be easier to solve, but one should not underestimate the difficulty of obtaining numerical solutions in the absence of a clear qualitative understanding of the behavior of the materials. 

Our earlier discussion of electronic wave functions for many-electron atoms drew attention to the main inadequacy of the Hartree-Fock single determinant treatment it does not take account of the correlation between the motions of electrons with opposite spins. In molecules this can even lead to qualitative deficiencies in the description of electronic structure, such as the failure to describe dissociation correctly. For example, the correct wave function for the singlet state of the hydrogen molecule at large... 

To demonstrate the potential of two-dimensional nonresonant Raman spectroscopy to elucidate microscopic details that are lost in the ensemble averaging inherent in one-dimensional spectroscopy, we will use the Brownian oscillator model and simulate the one- and two-dimensional responses. The Brownian oscillator model provides a qualitative description for vibrational modes coupled to a harmonic bath. With the oscillators ranging continuously from overdamped to underdamped, the model has the flexibility to describe both collective intermolecular motions and well-defined intramolecular vibrations (1). The response function of a single Brownian oscillator is given as,... 

The collinear model (Eq. (15)) has been successfully used in the semiclassical description of many bound and resonant states in the quantum mechanical spectrum of real helium [49-52] and plays an important role for the study of states of real helium in which both electrons are close to the continuum threshold [53, 54]. The quantum mechanical version of the spherical or s-wave model (Eq. (16)) describes the Isns bound states of real helium quite well [55]. The energy dependence of experimental total cross sections for electron impact ionization is reproduced qualitatively in the classical version of the s-wave model [56] and surprisingly well quantitatively in a quantum mechanical calculation [57]. The s-wave model is less realistic close to the break-up threshold = 0, where motion along the Wannier ridge, = T2, is important. 

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