Experimental Molecular Intensity Functions

Calcidation of Experimental Molecular Intensity Functions The total intensity, which is the sum of the molecular intensity and the background [c/. equation (18)], is obtained experimentally, usually firom photographic plates. In routine work the structure information is supposed to lie in Ita(s) only and to derive this function in a background, IiJls), must be found. The theoretical background, I s), may be calculated from (20). However, the theoretical background cannot in general be used for all s values because of systanatic errors (see p. 39). 

The background is usually not subtracted directly from the total intensity, 7 t(s), since certain advantages are obtained by dividing I (s) with I (s) giving a levelled intensity curve 

The levelled theoretical intensity curve is then obtained from (18) 

When K s) in equation (43) has been determined, the author usually calculates a modified molecular intensity function by subtracting K s) from nd multiplying the result with the expression necessary to obtain the experimental function corresponding to equation (30) or (36)  

Another possible procedure is to use the experimental background, /b (r), to calculate 

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In fact, information about the three-dimensional electron densities in molecules can be obtained more directly from the experimental intensity functions. Results for the Roux function (the difference between the molecular electron density and the sum of the electron densities of unperturbed atoms) have been given for diatomic molecules by Kohl and Bartell. ... 

Whatever the calculation procedure, the molecular intensity has to be obtained from the experiments. It is convenient to operate with a function I which is the experimental representation of the expression s. ... 

For some examples see (a) Bako, I. Radnai, T Belisant Funel, M. C. Investigation of structure of liquid 2,2,2-trifluoroethanol neutron diffraction, molecular dynamics, and ab initio quantum chemical study, J. Chem. Phys. 2004, 121, 12472-12480 (b) Cabaco, I. Danten, Y. Besnard, M. Guissani, Y. Guillot, B. Neutron diffraction and molecular dynamics study of liquid benzene and its fluorinated derivatives as a function of temperature, J. Phys. Chem. 1997, BlOl, 6977-6987. This last paper has a clear description of the derivation of pair correlation functions from experimental scattered intensities from liquids. 

We now have a quantitative intensity function free from experimental aberrations. The remaining sections are concerned with detailing how such functions may be used to extract useful and detailed structural information relating to the local molecular organization of noncrystalline polymers. 

The distance of each reflection from the center of the pattern is a function of the fiber-to-film distance, as well as the unit-cell dimensions. Therefore, by measuring the positions of the reflections, it is possible to determine the unit-cell dimensions and, subsequently, index (or assign Miller indices to) all the reflections. Their intensities are measured with a microdensitometer or digitized with a scanner and then processed.8-10 After applying appropriate geometrical corrections for Lorentz and polarization effects, the observed structure amplitudes are computed. This experimental X-ray data set is crucial for the determination and refinement of molecular and packing models, and also for the adjudication of alternatives. 

The ability of a dendritic shell to encapsulate a functional core moiety and to create a specific site-isolated microenvironment capable of affecting the molecular properties has been intensively explored in recent years [19]. A variety of experimental techniques have been employed to evidence the shielding of the core moiety and to ascertain the effect of the dendritic shell [19, 20]. Dendrimers with a fullerene core appear to be appealing candidates to evidence such effects resulting from the presence of the surrounding dendritic branches. Effectively, the lifetime of the first triplet excited state of fullerene derivatives... 

The mass attenuation coefficient values of the elements are available in the literature [46]. Therefore, the mass attenuation coefficient of a compound can be calculated. Thus and (in Eq. 15) can be calculated provided the molecular formulas of components 1 and 2 are known. It is then possible to calculate the intensity ratio, /u/(/ii)o> as a function of xx. This ratio can also be experimentally obtained. The intensity of peak i of a sample consisting of only 1 is determined [(/ii )o] This is followed by the determination of the intensity of the same peak in mixtures containing different weight fractions of 1 and 2. This enables the experimental intensity ratio, /n/(/n)o, to be obtained as a function of xx. The principles discussed above formed the basis for the successful analyses of quartz-beryllium oxide and quartz-potassium chloride binary mixtures [45]. 

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