Crystal structure deduction

An experimental study of barbituric acid found one new polymorph where molecules in the asymmetric unit adopted two different conformations [10]. The conformational aspect was investigated through the use of ab initio calculations, which permitted the deduction that the new form found would have a lower lattice energy than would the known form. It was also found that many hypothetical structures characterized by a variety of hydrogen-bonding structures were possible, and so the combined theoretical and experimental studies indicated that a search for additional polymorphs might yield new crystal structures. 

A piperidene-based intermediate was found to crystallize as either an anhydrate or a hydrate, but the impurity profile of the crystallized solids differed substantially [26], Considerations of molecular packing led to the deduction that there was more void volume in the anhydrate crystal structure than in that of the hydrate form, thereby facilitating more clathration in the anhydrate than in the hydrate phase. This phenomenon was led to a decision to crystallize the hydrate form, since lower levels of the undesired impurity could be occluded and greater compound purity could be achieved in the crystallization step. 

The two starting components were packed into a glass capillary from opposite ends until they met in the centre. A coloured reaction product was observed visually after 7 to 10 min at the reactant interface. As time progressed, the product interface was observed to advance in the direction of the picric acid reactant. Further study of this reaction supported a vapour diffusion mechanism, bolstered in part by the observation that complexation proceeds even if a small gap of space exists between the two reactants [12]. The nature of the complex was investigated in additional work, whereby it was proposed that a donor/acceptor 71-complex was produced [13]. A crystal structure confirming this deduction was later published [14]. 

The first belongs to space group Fm3m, and the latter to I 43m, and these two possibilities can be distinguished by comparing the X-ray diffraction intensities expected from the two structure types with those actually observed. This type of deduction is based on consideration of the roles of the individual atoms in a crystal structure, which usually finds application in compounds of inorganic composition such as binary and ternary compounds, alloys, and minerals. 

Takeuchi, Y., Nowacki, W. Detailed crystal structure of rhombohedral M0S2 and systematic deduction of possible polytypes of molybdenite. Schweiz. Mineral. Petrog. Mitt. 44, 105—... 

The X-ray crystal structure determination of quebrachamine reveals that the conformation adopted by the molecule is one in which the lone electrons on Nb are sterically shielded by other atoms if this conformation is preferred in solution, the reluctance of quebrachamine to form quaternary salts is explained.114 This conclusion agrees with that derived from 13C n.m.r. spectroscopy,us which in turn is consistent with deductions made earlier on the basis of 3H n.m.r. spectroscopy. 

Takeuchi, Y. and Nowacki, W., Detailed Crystal Structure of Rhombohedral M0S2 and Systematic Deduction of Possible Polytypes of Molybdenite, Schweiz Mineral. Petrographische Mittellungen, 44, 105, (1964). 

We have now shown, by three different approaches, that if one knows the atomic coordinates xj, yj, Zj of all of the atoms j in a unit cell, and their scattering factors fj, then one can precisely predict the amplitude and phase of the resultant wave scattered by a specific family of planes hkl. We can calculate this for any and all families of planes in the crystal, hence the amplitude and phase can be calculated for every structure factor in the X-ray diffraction pattern. Given the structure of a crystal, namely the coordinates of the atoms in the unit cell, we can predict the entire diffraction pattern, the entire Fourier transform of the crystal. This is an enormously powerful statement. It means that if, by some means, we can deduce the positions of the atoms in a crystal structure, then we can immediately check the correctness of that deduction by seeing how well we can predict the relative values of the intensities in the diffraction pattern. 

All methods of deduction of the relative phases for Bragg reflections from a protein crystal depend, at least to some extent, on a Patterson map, commonly designated P(uvw) (46, 47). This map can be used to determine the location of heavy atoms and to compare orientations of structural domains in proteins if there are more than one per asymmetric unit. The Patterson map indicates all the possible relationships (vectors) between atoms in a crystal structure. It is a Fourier synthesis that uses the indices, l, and the square of the structure factor amplitude f(hkl) of each diffracted beam. This map exists in vector space and is described with respect to axes u, v, and w, rather than x,y,z as for electron-density maps. 

Besides its deduction from crystal structure analyses the formation of five-membered rings is also evident from the Si NMR spectra. The incorporation into a five-membered ring causes a strong... 

Assign positions to aU atoms and list the positional parameters which uniquely define the crystal structure. Explain your deductions concisely. 

Goldschmidt predicted from his empirical rule that calcium chloride would not have the fluorite structure, and he states that on investigation he has actually found it not to crystallize in the cubic system. Our theoretical deduction of the transition radius ratio allows us to predict that of the halides of magnesium, calcium, strontium and barium only calcium fluoride, strontium fluoride and chloride, and barium fluoride, chloride,... 

The problem of estimating crystal field parameters can be solved by considering the CFT/LFT as a special case of the effective Hamiltonian theory for one group of electrons of the whole A -electronic system in the presence of other groups of electrons. The standard CFT ignores all electrons outside the d-shell and takes into account only the symmetry of the external field and the electron-electron interaction inside the d-shell. The sequential deduction of the effective Hamiltonian for the d-shell, carried out in the work [133] is based on representation of the wave function of TMC as an antisymmetrized product of group functions of d-electrons and other (valence) electrons of a complex. This allows to express the CFT s (LFT s or AOM s) parameters through characteristics of electronic structure of the environment of the metal ion. Further we shall characterize the effective Hamiltonian of crystal field (EHCF) method and its numerical results. 

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