Bandshapes

Dubai H-R and Quack M 1980 Spectral bandshape and intensity of the C-H chromophore in the... 

Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1)...

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]. 

Kevra, S. A. Bergman, D. L. Maloy, J. T. A Gomputational Introduction to Ghromatographic Bandshape Analysis, ... 

Several factors affect the bandshapes observed ia drifts of bulk materials, and hence the magnitude of the diffuse reflectance response. Particle size is extremely important, siace as particle size decreases, spectral bandwidths generally decrease. Therefore, it is desirable to uniformly grind the samples to particle sizes of <50 fim. Sample homogeneity is also important as is the need for dilute concentrations ia the aoaabsorbiag matrix. 

The distribution of the vectors normal to the surface is particularly interesting since it can be obtained experimentally. The nuclear magnetic resonance (NMR) bandshape problem, for polymerized surfaces, can be transformed into the mathematical problem of finding the distribution function f x) of... 

Then, in complex molecules where many bending modes may participate to a Fermi resonance, we can expect the Vs (X-H Y) bandshape to be perturbed in a very complex way. It is also of importance to note that the perturbation due to a sole Fermi resonance is delocalized on the whole vs (X-H - -Y) band. 

Of course, varying the damping parameters allows the bandshapes to evolve between these three limiting cases. 

Besides, we have shown elsewhere [22,23,71,72] that the term Fermi resonances is not fully adequate because noticeable perturbations of the vs (X-H Y) bandshape may be obtained in nonresonant cases—that is when the Fermi coupling takes place between the fast mode (of frequency 0)o) and a bending mode whose overtone frequency 2g>s may be very far from 0)o (see Section IV.B.3). 

Class C Fluorophores that undergo no photoinduced proton transfer but only photoinduced electron transfer. The fluorescence quantum yield of these fluorophores is very low when they are in the non-protonated form because of internal quenching by electron transfer. Protonation (which suppresses electron transfer) induces a very large enhancement of fluorescence (see Section 10.2.2.5). The bandshapes of the excitation and fluorescence spectra are independent of pH. 

Mention should be made here of recent attempts by Piepho, Schatz and Krausz (46) to give a general interpretation of intervalence bandshapes in terms of a Hamiltonian equivalent to that of eq 6. They use vibronic eigenfunctions (following the method of solution of Merrifield (47)) rather than adiabatic Born-Oppenheimer (ABO) functions. Thus, the aim is to interpret an observed spectrum in terms of one vibrational coupling mode, which is antisymmetric. Their analysis of the spectrum of the Creutz-Taube ion yields a value of 0 of 1.215, i.e., a rather weakly localized ground state. Using their assumed unperturbed... 

A Gaussian bandshape results when the partition coefficient, K (= Cs/Cm), is independent of the concentration of solute on the column. In real columns, K changes as the concentration of solute increases, and bandshapes are skewed.10 A graph of Cs versus Cm (at a given temperature) is called an isotherm. Three common isotherms and their resulting bandshapes are shown in Figure 23-20. The center isotherm is the ideal one, leading to a symmetric peak. 

Figure 23-20 Common isotherms and their resulting chromatographic bandshapes.

Describe how nonlinear partition isotherms lead to non-Gaussian bandshapes. Draw the bandshape produced by an overloaded column and a column with tailing. 

For numerical simulation of skewed bandshapes, see S. Sugata and Y. Abe, An Analogue Column Model for Nonlinear Isotherms The Test Tube Model, ... 

Spectral lineshapes were first expressed in terms of autocorrelation functions by Foley39 and Anderson.40 Van Kranendonk gave an extensive review of this and attempted to compute the dipolar correlation function for vibration-rotation spectra in the semi-classical approximation.2 The general formalism in its present form is due to Kubo.11 Van Hove related the cross section for thermal neutron scattering to a density autocorrelation function.18 Singwi et al.41 have applied this kind of formalism to the shape of Mossbauer lines, and recently Gordon15 has rederived the formula for the infrared bandshapes and has constructed a physical model for rotational diffusion. There also exists an extensive literature in magnetic resonance where time-correlation functions have been used for more than two decades.8... 

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