Diffraction methods theoretical basis

This concise treatise is not intended to make readers experts on hardcore crystallography, but to help them to get a qualitative picture of the method and understand the underlying principles and dra vbacks of single crystal X-ray diffraction analysis. To study the theoretical basis of X-ray crystallography in detail, the reader is encouraged to read some excellent X-ray crystallography text books to become fully acquainted vith the theory involved at introductory [10], intermediate [11] or advanced [12] level. 

As usual in stereochemical research, four main approaches have been applied to the problem of assigning chiralities to optically active cyclophanes. They are listed in order of their reliabilities i) anomalous X-ray diffraction (Bijvoet method), ii) chemical correlations with compounds of known chiralities (preferably established by the Bijvoet method), iii) kinetic resolutions and/or asymmetric syntheses, iv) interpretation of chiroptical properties (mainly circular dichroism) on the basis of (sector) rules including theoretical methods. 

Measurement of electron density by X-ray diffraction cannot distinguish each electron in different orbitals however, it provides overall information on the asphericity of the d electron distribution in a molecule as well as on the redistribution of electrons upon chemical bond formation. At the present stage, experimental charge distributions can be compared only qualitatively with theoretical calculations. The method, however, will be of considerable value in clarifying poorly understood bonding situations. If the electron-density distribution and the geometrical arrangement of the atomic nuclei in a complex are known, it is possible, at least in principle, to predict all its physical and chemical properties on the basis of quantum mechanics. 

The protein-solvent interface was studied in an explicit solvent environment of 3182 water molecules by MD simulations performed on metmyoglobin [31].Both the structure and dynamics of the hydrated surface of myoglobin are similar to that obtained by experimental methods calculating three-dimensional density distributions, temperature factors and occupancy weights of the solvent molecules. On the basis of trajectories they identified multiple solvation layers around the protein surface including more than 500 hydration sites. Properties of theoretically calculated hydration clusters were compared to that obtained from neutron and X-ray data. This study indicates that the simulation unified the hydration picture provided by X-ray and neutron diffraction experiments. 

Added in Proofs, Combined X-ray and electron diffraction data can be used to analyze the electron density in a molecule. Identification of the square of the wave function with the electron density then gives the coefficients of the basis atomic orbitals in the various molecular orbitals, and therefore permits the evaluation of the electron populations. This method was used for instance with 1,3,5-trimethyl-benzene, and good agreement with theoretical data was obtained [B. H. O Connor,... 

Deviations from predicted behaviour are here interpreted in terms of solvation, but other factors such as ion association may also be involved. Ion association leads to deviations in the opposite direction and so compensating effects of solvation and ion association may come into play. The deviations may also be absorbing inadequacies of the Debye-Hiickel model and theory, and so no great reliance can be placed on the actual numerical value of the values emerging. This major method has now been superseded by X-ray diffraction, neutron diffraction, NMR and computer simulation methods. The importance of activity measurements may lie more in the way in which they can point to fundamental difficulties in the theoretical studies on activity coefficients and conductance. The estimates of ion size and hydration studies could well provide a basis for another interpretation of conductance and activity data, or to modify the theoretical equations for mean activity coefficients and molar conductivities. 

The single BHC isomers differ substantially from one another with respect to their solubility in organic solvents. This enables their separation by fractional crystallisation and fractional extraction. Subsequent determination of the structure of the isomers was established by X-ray diffraction, electron diffraction and spectrophotometric methods, on the basis of differences in their dipole moments and chemical reactions, and by theoretical considerations (Orloff, 1954 Bastiansen and Hassel, 1947 Whitney and Corvin, 1949 Bastiansen et al., 1949 Hassel and Ottar, 1950 Hughes et al.. 1953). 

In seventies XRD methods gained still greater popularity as the Rietveld [223] program was introdueed. On the basis of the stmeture of all clinker phases the theoretical X-ray pattern can be ealculated, which then is eompared with the diffraction pattern of examined sample and correlated using the least square method. This method needs, however, the calibration curves determination for different clinker types, in order to take into aeeount the matrix influence. 

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