Density data set

The advent of CCD detectors for X-ray diffraction experiments has raised the possibility of obtaining charge density data sets in a much reduced time compared to that required with traditional point detectors. This opens the door to many more studies and, in particular, comparative studies. In addition, the length of data collection no longer scales with the size of the problem, thus the size of tractable studies has certainly increased but the limit remains unknown. Before embracing this new technology, it is necessary to evaluate the quality of the data obtained and the possible new sources of error. The details of the work summarized below has either been published or submitted for publication elsewhere [1-3]. 

READ STATE-DENSITY DATA SETS, AND STORE NUMBER OF STATES AND STATE DENSITIES IN SPDNOS> AND ACCORDING TO ... 

Fig. 7.10 a Response time needed to complete a change of AR = (Rco — Ro)/2 obtained from fitting the transient curves with Eq. 7.3. The nontemplated and DG-stmctured film were electropoly-merized under the same conditions including the same total current density. Data sets a and b correspond to exposures to 1.2 and 3.8 % of ethanol vapor in dry nitrogen, respectively, b Sensitivity of nontemplated and DG-stmctured film as function of the partial ethanol pressure. Alexandre Nicolas analyzed the data and prepared the present graphs [7]... 

If sufficienf resulfs are available if is useful to identify any potential outliers in the data and determine if these indicate occasional peaks or could be representative of more persisfenf peaks (see Section 5.10). This is difficulf with a low density data set. 

The second category differs from those discussed above in that it relates, in the main, to those situations for which no data or only characterizing data exist. In such cases, this small set of characterizing data or, in its absence, stmcture data are used to estimate a set of parameters of the type requited by point generation routines. One notable specific example of this type of facihty is the creation of data sets for petroleum boiling fractions from information on average boiling point and density. 

As this example illustrates, plots such as these can be useful for providing a qualitative understanding of the electron density and its relationship to reactivity, but you would be wise to use and interpret them with care. It is all too easy to unintentionally manipulate such illustrations to create the effect that one expects to observe. For example, any one slice or isosurface of the electron density can be used to argue for a given viewpoint. It is important to examine and visualize the entire volumetric data set before reaching conclusions based on it. ... 

There are two types of data necessary to obtain accurate global estimates of vegetation carbon pools or biomass. First, it is important to have accurate data on the areal extent of major ecosystems. Matthews (29) found that calculations of global biomass were significantly influenced by the land cover data set used. Second, there must be accurate estimates of biomass density for terrestrial ecosystems. There is a wide range of estimates published for the same ecosystem, each derived by different methods (29), and none having statistical reliability (7). 

Step 1. Obtain AT, the range of temperatures covered by the data set. Step 2. For each density value, p, in the set, calculate, ... 

Errors in the low-density regions of the crystal were also found in a MaxEnt study on noise-free amplitudes for crystalline silicon by de Vries et al. [37]. Data were fitted exactly, by imposing an esd of 5 x 10 1 to the synthetic structure factor amplitudes. The authors demonstrated that artificial detail was created at the midpoint between the silicon atoms when all the electrons were redistributed with a uniform prior prejudice extension of the resolution from the experimental limit of 0.479 to 0.294 A could decrease the amount of spurious detail, but did not reproduce the value of the forbidden reflexion F(222), that had been left out of the data set fitted. 

Finally, recent work of Iversen et al. has carefully examined the bias associated to the accumulation of the error on low-order reflexions, and attempted a correction of the MaxEnt density [39]. The study, based on a number of noisy data sets generated with Monte Carlo simulations, has produced less non-uniform distribution of residuals, and has given quantitative estimate of the bias introduced by the uniform prior prejudice. For more details on this work, we refer the reader to the chapter by Iversen that appears in this same book. 

If these structural features are not well represented by a mild redistribution of random independent constituents from an initially given prior prejudice, and arise instead from some degree of correlation between the scatterers, they cannot be expected to be satisfactorily dealt with by the method. For these reasons, substructures which scatter well beyond the experimental resolution should be left out of the subset of scatterers distributed at random. The data sets commonly collected for charge density studies do not as a rule extend beyond 0.4 A resolution, but scattering from the atomic core does extend well beyond this limit.2... 

Takata, M. and Sakata, M. (1996) The influence of completeness of the data set on the charge density obtained with the maximum-entropy method. A re-examination of the electron-density distribution in Si, Acta Cryst., A52, 287-290. 

The MEM is a powerful new method which is especially useful in cases with limited data sets (powder diffraction). Monte Carlo simulations have shown that the MEM introduces systematic features into the reconstructed density and caution should be exercised when interpreting fine details of an MEM density. It must be emphasized that because the present MEM algorithms do not contain any models, they cannot filter out inconsistencies in the data stemming from systematic errors. The MEM densities may therefore contain non-physical features not only because of systematic bias in the calculation but also because of systematic errors in the data. 

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