Crystal discovery approaches

After the discovery of the first mesoporous silicas through external templating, a lot of work has been done to understand and rationalize the formation mechanisms of these materials. Numerous research groups employed a variety of techniques (e.g., NMR spectroscopy. X-ray diffraction, cryo-TEM, electron paramagnetic resonance, and fluorescence) toward this objective. Several models have been proposed [10] and two of them are generally accepted the liquid crystal templating approach and the cooperative self-assembly approach. In both models, the interactions between the surfactant molecules and the inorganic species direct the formation of the ordered solid. 

The crystal structures in Chapters 5 and 6 were determined by x-ray diffraction, and the papers illustrate Pauling s approach to this experimental technique, including his most notable methodological contributions—the coordination method (SP 42) and the stochastic method (SP 47). In its day, SP 47 was a tour de force in the determination of a complex crystal structure. SP 46 contains Pauling s famous discovery of two quite different crystal structures giving the same x-ray diffraction pattern, which violated the then-current conventional wisdom in x-ray crystallography. 

There are two approaches to the solution of the phase problem that have remained in favor. The first is based on the tremendously important discovery or Patterson in the 1930s ihal the Fourier summation of Eq. 3. with (he experimentally known quantities F2 (htl> replacing F(hkl) leads nol to a map of scattering density, but to a map of all interatomic vectors. The second approach involves the use of so-called direct methods developed principally by Karie and Hauptman of the U.S. Naval Research Laboratory and which led to the award of the 1985 Nobel Prize in Chemistry. Building upon earlier proposals that (he relative intensities of the spots in a diffraction pattern contain information about a crystal phase. Hauptman and Karie developed a mathematical means of extracting the information. A fundamental proposition of (heir direct method is that if thrice intense spots in the pattern have positions whose coordinates add up to zero, their relative phases will cancel out. Compulations done with many triads of spots yield probable phases for a significant number of diffracted waves and further mathematical analysis leads lo a likely solution for the structure of the molecule as a whole. 

The vitamin was discovered in liver as the antipemi-cious anemia factor in 1926, but discovery of its complete structure had to await its purification, chemical characterization, and crystallization, which required more than 20 years. Even then the determination of such a complex structure proved to be an elusive goal by conventional approaches of that day and had to await the elegant x-ray crystallographic study of Lenhert and Hodgkin in 1961, for which Dorothy Hodgkin was awarded the Nobel Prize in 1964. 

Since its discovery by Pasteur in 1853,5 classical resolution by selective crystallization of diastereo-isomers, despite wide and frequent use, remains to a large degree a method of trial and error. Various attempts to rationalize classical resolutions and predict a successful combination of race-mate and resolving agent by computational approaches so far have not been crowned with remarkable success.6 Even when the crystal structures of both diastereoisomeric salts are known, molecular modeling calculations do not provide a basis for a reliable prediction. Only recently has some progress been made in the calculation of the relative thermodynamic stability of ephedrine-cyclic phosphoric acid 4 diastereoisomers,7 a diastereoisomeric salt frequently used as a model system (vide infra). 

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