Computing Problems and Methods in X-Ray Crystallography

Publisher Summary This chapter presents computing problems and general computational methods in X-ray crystallography, including structure factor calculation, Fourier series calculation, differential synthesis refinement, least-squares, Patterson methods, and phase problem X-ray crystallography. It examines the chemical structures of crystalline substances through the X-ray diffraction patterns of the crystals. The crystal structures are solved by postulating an arrangement of atoms in an infinite crystal lattice and comparing the calculated diffraction pattern from the crystal of the unknown. When the observed and calculated patterns agree fairly well, and the postulated structure is chemically reasonable, a trial solution for the structure is obtained. The parameters defining this trial structure are refined against the observed diffraction data to confirm the solution and to extract any other physical information about this particular crystal structure, which is contained in the data. Trial structures are evaluated through use of Fourier series summations, for which computers are usually a necessity, and the refinement is done using Fourier series or least-squares method. A skeletal sketch of the data and basic formulas of crystallography are provided.

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