Structure determination systematic absences

Distinguishing Space Groups by Systematic Absences. From the symmetry and metric properties of an X-ray diffraction pattern we can determine which of the 6 crystal systems and, further, which of the 11 Laue symmetries we are dealing with. Since we need to know the specific space group in order to solve and refine a crystal structure, we would still be in a highly unsatisfactory situation were it not for the fact that the X-ray data can tell us still more. 

Nonetheless, analysis of the systematic absences (the complete list is found in Table 2.12 to Table 2.17) usually allows one to narrow the choice of space group symmetry to just a few possibilities, and the actual symmetry of the material is usually established in the process of the complete determination of its crystal structure. Especially when powder diffraction data are used, it only makes sense to analyze low angle Bragg peaks to minimize potential influence of the nearly completely overlapped reflections with indices not related by symmetry. An example of the space group determination is shown in Table 2.11. 

It is possible from measurements of a limited number of reciprocal-lattice vectors and observations of systematic absences of reflections to deduce not only the shape and dimensions of the unit cell, but also the complete symmetry of the crystal structure. The determination of the complete structure now requires the contents of the unit cell to be deduced from the intensities of the reflections . These are usually determined by using diffractometers rather than film to record the diffraction. A diffractometer is usually a device that allows the recording of the intensity of scattering in any particular direction in space. Modern types, using CCD arrays, can determine the intensity over a range of directions for one setting of the instrument. This greatly speeds up the collection of data but leads to some complication in terms of the need to calibrate the different... 

The process of structure solution of an unknown material from powder data can be divided into several steps. First one must record the highest-quality data possible on a (ideally) pure sample. One must then determine the unit cell parameters from observed peak positions (several software packages exist to tackle this nontrivial step). The space group symmetry must then be determined from systematic absences. At this stage, one of a number of different routes can be followed. One... 

To verify (or disprove) the polymeric structure of the series of In (III) and Tl (HI) porphyrins, the X-ray crystal structure of T1(TPP)F was determined. A suitable crystal of T1(TPP)F was obtained, by slow diffusion of pentane into a solution of the compound in methylene chloride. Preliminary Weissenberg photographs along the c axis revealed a four-fold symmetry, and from the systematic absences of hOl (h+1 = 2n), OkO (k=2n), and from the subsequent least-squares refinement, the space group was determined to be P2j/n. 

Whenever = 2n- -l, with n integer, exp[7riA ] = —1 and the structure factor vanishes. Thus, the above list of observed structure factors is indeed a direct experimental proof that in the crystal of succinic anhydride any scatterer atx,y,z has an equivalent scatterer at -x, 1/2 -b y, 1/2 - z. The same applies to (hOO) and (00/) reflections because of the other two equivalent positions of the space group. Internal symmetry is revealed by destructive interference of scattered waves from symmetry-related objects. In fact, the analysis of systematic absences is the method normally used for determining the space group from diffraction patterns. 

Similarly, improvement in the accuracy of the nuclear dynamics would be fruitful. While in this review we have shown that, in the absence of any approximations beyond the use of a finite basis set, the multiple spawning treatment of the nuclear dynamics can border on numerically exact for model systems with up to 24 degrees of freedom, we certainly do not claim this for the ab initio applications presented here. In principle, we can carry out sequences of calculations with larger and larger nuclear basis sets in order to demonstrate that experimentally observable quantities have converged. In the context of AIMS, the cost of the electronic structure calculations precludes systematic studies of this convergence behavior for molecules with more than a few atoms. A similar situation obtains in time-independent quantum chemistry—the only reliable way to determine the accuracy of a particular calculation is to perform a sequence of... 

A systematic investigation of the free amino acids of the Leguminosae led to the isolation of a novel ninhydrin-positive compound from the leaves of Derris elliptica Benth. (Papilionidae) (93). This substance was analyzed as C6H,3N04 (microanalysis and high resolution mass spectrometry) and was shown to be an amino alcohol. The absence of a carbonyl in the 1R, the loss of 31 mass units in the mass spectrum, and a positive periodate cleavage reaction were best embodied into a dihydroxydihydroxymethylpyrrolidine structure. The relative simplicity of the NMR spectra (three peaks in the 13C spectrum four spin-system in the H spectrum) pointed out a symmetrical structure. Inasmuch as the material was optically active ([a]D 56.4, c = 7, H20), meso structures were ruled out, and the 2R, 3R, 4R, 5R relative configuration was retained (93). This structure (53) was further confirmed by an X-ray determination (94). 

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