Derivative peak searches

The crystal used for data coUection was transferred to an Enraf-Nonius CAD-4 diffractometer. Automatic peak search and indexing procedures yielded the same monoclinic cell as derived from the X-ray powder diffraction data and precession photographs. Testing showed that the cell was indeed primitive and that there was no superlattice present. Table 5 gives the crystal data and X-ray experimental parameters, and Table 6, the interatomic distances and angles. Positional and thermal parameters are given in Table S3 (Supporting Information)... 

The coordinates of atomic positions can be located and a molecular model derived, either by contouring the map, or by use of a peak search routine.. An example is provided in Figure 9.6. In the most favorable cases this map will also give an indication of the locations of atoms that were not included in the phasing model. Such a map can also be used to improve the accuracy of a preliminary model by adjusting the model to best fit the electron density. 

An automatic peak search is actually the simplest (one-dimensional) case in the more general two- or three-dimensional image recognition problem. Image recognition is easily done by a human eye and a brain but is hard to formalize when random errors are present and, therefore, difficult to automate. Many different approaches and methods have been developed two of them are most often used in peak recognition and will be discussed here. These are the second derivative method and the profile scaling technique. 

Figure 4.8. Automatic peak search conducted using a second derivative method (top) and manually corrected reduced pattern (bottom). The upward arrow placed on the digitized pattern shows a false peak (which was eliminated manually) and the downward arrows show the missed peaks (which were added manually).

Figure 4.7 Example of the Ka2 stripping for the quartz quintuplet (3 ai/a2 doublets) at 20 = 68°. Top list of raw data (count numbers for 0.02° step width). Middle unsmoothened pattern with constructed background. Bottom result of Ka2 stripping, background subtraction and 5 point smoothing. Also drawn is the 2nd derivative, which was used for the peak search (found positions indicated).

The peak search by 2nd derivatives represents a kind of sharpening (deconvolution), i.e. a division by the Fourier transform of a certain peak shape in the frequency domain. This is possible only if this Fourier transform has no zeroes, i.e. if it monotonically approaches zero. Bromba and Ziegler (1984) report such an algorithm, but its usability for X-ray patterns was not proved until now. 

T. C. Huang and W. Parrish, A combined derivative method for peak search analysis, Adv. X-Ray Anal., 1984, 27, 45-52. 

The position can be determined either from information derived from the peak location or by taking account of library data which indicate which peaks to expect within the particular multiplet. Both have their advantages and disadvantages. Obviously, unless a gamma-ray is in a library then it will not be taken account of and so a simple library directed approach cannot cope with the unexpected. On the other hand, small peaks within a multiplet and very close multiples may not be resolved by the peak search and incorrect peak areas may again result. 

The fact that each monosaccharide may give more than one peak owing to the formation of anomeric derivatives has led to a search for means to eliminate this complication. The anomeric center may be removed either by conversion into the oxime5 or the nitrile,394,3943 by oxidation followed by formation of the lactone (see Section IX, p. 71), or by reduction to the alditol. The last method is simpler than oxidation, and the separation of alditols and of aldononitriles will be discussed here additional examples are given in Table V (see p. 119). The early work on the separation of alditols has been discussed by Bishop.4 The necessity of decomposing borate complexes... 

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