Structure determination, experimental diffraction-based methods

The value in using diffraction based methods for the determination of phase abundance arises from the fact that diffraction information is derived directly from the crystal structure of each phase rather than from secondary parameters such as measurement of total chemistry. However, the methodology of quantitative phase estimation is fraught with difficulties, many of which are experimental or derive from sample related issues. Hence it is necessary to verify diffraction based phase abundances against independent methods. In those circumstances where this is not possible, the QPA values should be regarded only as semi-quantitative. While such values may be useful for deriving trends within a particular system, they cannot be regarded as an absolute measure. 

The experimental studies on biopolymer structures are increasingly supplemented by computational approaches. First, it has to be realized that computation is a sine qua non for experimental structure determination by diffraction methods and NMR spectroscopy themselves. In addition, independent computational studies can provide useful information on structure and dynamics of biopolymers not accessible, at least currently, by experiments. With regard to base poiyads there are three fields that have to be mentioned here primarily quantum-chemical studies of nucleic building blocks, MD simulations of medium-sized nucleic acids and structural bioinformatics. 

Valence shell electron pair repulsion theory (VSEPR) provides a method for predicting the shape of molecules, based on the electron pair electrostatic repulsion. It was described by Sidgwick and Powell" in 1940 and further developed by Gillespie and Nyholm in 1957. In spite of this method s very simple approach, based on Lewis electron-dot structures, the VSEPR method predicts shapes that compare favorably with those determined experimentally. However, this approach at best provides approximate shapes for molecules, not a complete picture of bonding. The most common method of determining the actual stmctures is X-ray diffraction, although electron diffraction, neutron diffraction, and many types of spectroscopy are also used. In Chapter 5, we will provide some of the molecular orbital arguments for the shapes of simple molecules. 

Besides the classical techniques for structural determination of proteins, namely X-ray diffraction or nuclear magnetic resonance, molecular modelling has become a complementary approach, providing refined structural details [4—7]. This view on the atomic scale paves the way to a comprehensive smdy of the correlations between protein structure and function, but a realistic description relies strongly on the performance of the theoretical tools. Nowadays, a full size protein is treated by force fields models [7-10], and smaller motifs, such as an active site of an enzyme, by multiscale approaches involving both quantum chemistry methods for local description, and molecular mechanics for its environment [11]. However, none of these methods are ab initio force fields require a parameterisation based on experimental data of model systems DPT quantum methods need to be assessed by comparison against high level ab initio calculations on small systems. 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a statistical description of the structure may be obtained. The so-called radial distribution function is defined as ... 

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