Interatomic distances 522 Subject

We can now proceed to the generation of conformations. First, random values are assigne to all the interatomic distances between the upper and lower bounds to give a trial distam matrix. This distance matrix is now subjected to a process called embedding, in which tl distance space representation of the conformation is converted to a set of atomic Cartesic coordinates by performing a series of matrix operations. We calculate the metric matrix, each of whose elements (i, j) is equal to the scalar product of the vectors from the orig to atoms i and j ... 

We underline these results and the implied concepts quoting from a comprehensive review on this subject (Simon 1983). We remember indeed that, ever since it was experimentally possible to determine atomic distances in molecules and crystals, efforts have been made to draw conclusions about the nature of the chemical bonding, and to compare interatomic distances (dimensions) in the compounds with those in the chemical elements. Distances between atoms in an element can be measured with high precision. As such, however, they cannot be simply used in predicting interatomic distances in the compounds. In a rational procedure, reference values (atomic radii) have to be extracted from the individual (interatomic distances) measured values. Various functions have been suggested for this purpose. In the specific case of the metals it has been pointed out that interatomic distances depend primarily on the number of ligands and on the number of valence electrons of the atoms (Pearson 1972). 

The atomic radius of an element is considered to be half the interatomic distance between identical (singly bonded) atoms. This may apply to iron, say, in its metallic state, in which case the quantity may be regarded as the metallic radius of the iron atom, or to a molecule such as Cl2. The difference between the two examples is sufficient to demonstrate that some degree of caution is necessary when comparing the atomic radii of different elements. It is best to limit such comparisons to elements with similar types of bonding, metals for example. Even that restriction is subject to the drawback that the metallic elements have at least three different crystalline arrangements with possibly different coordination numbers (the number of nearest neighbours for any one atom). 

HDS catalysts have been characterized extensively with a wide variety of tools, and several extensive reviews of the subject have been presented (85,88-91). Substantial effort has been aimed at relating catalytic activity and selectivity to microscopic properties such as catalyst composition, electronic structure, and geometric structure. EXAFS investigations of working catalysts have provided information about the composition, average local coordination, and interatomic distances of atoms in the catalyst clusters. It has been concluded that the active phase under operating conditions is MoS2-like particles with a dimension of 10—20 A (92-94). 

X-ray diffraction methods have also been used in the study of the structures of liquids. The continual movements which occur in liquids do not affect the determination of the principal interatomic distances. For earlier work on the subject see Randall s book (1934). Among later papers, those of Harvey (1939) on ethanol and Bray and Gingrich (1943) on carbon tetrachloride are typical. 

PETN usually forms needle or column-shaped crystals, in which state it pours with difficulty. It is however possible to produce cubic crystals, which pour easily, by recrystallization from ethyl acetate. PETN has been subjected to many crystallographic studies. On the basis of X-ray measurements carried out by Booth and Llewellyn [9] the interatomic distances have been shown to be ... 

The use of electron beams for diffraction studies on gases or vapours is one of the best known methods for the accurate determination of interatomic distances in simple molecules. There is an extensive literature on this subject, and no attempt will be made here to describe the method. A recent review article by Bastiansen and Skancke (1961) describes the method fully and illustrates the precision that can now be attained in the determination of intemuclear distances. 

The deformation of a material when subjected to a constant stress is, as discussed, usually time-dependent. At times of c. 10 6 s and less all materials, including liquids, have shear compliances (i.e shear/shear stress) of c. 10 n to 10"9 m2 N-1. This is because there is only sufficient time available for an alteration of interatomic distances and bending of bond angles to take place, and the response of all materials is of the same order of magnitude in this respect. Hie time required for the various structural units of a material to move into new positions relative to one another depends on the size and shape of the units and the strength of the bonds between them. 

It is certainly not by chance that Barriol s first research, in collaboration with Pierre Donzelot, dealt with the Raman effect. Lespieau had been one of the first who had studied, often with Maurice Bourguel, the Raman effect, [9] in relation to chemical constitution. [10] Donzelot did some research on the same subject with Charles Prevost, another student of Lespieau, when Prevost was a professor of chemistry at the Nancy Faculte de Pharmacie. At the very same time Barriol also was around. A note to the Academic, des Sciences, concerning the relation between Raman frequencies and interatomic distances, by Donzelot and Barriol, was presented by Lespieau and concluded It seems that the interatomic distance constitutes an essential characteristic of a molecule, around which one can group the properties, not only those related to the Raman effect, but also manyfold physical characteristics. [11]... 

It is emphasized here that the accurate determination of the interatomic distances are a prerequisite to achieve the three-dimensional structure of peptides, proteins and macromolecules. A protocol for REDOR and RR experiments for this purpose is described in depth from both the theoretical and practical points of view. In addition, a systematic procedure to construct the three-dimensional structure from these distance constraints is described together with a brief review of some related subjects so far reported. We believe that the measurement of accurate interatomic distances can be the most promising and valuable means to reveal the three-dimensional structure of macromolecules such as membrane proteins in the future. 

It is clear that from the observed interionic distances we can deduce only the sum of two ionic radii, but that if any one radius is known then other radii may be found. Various independent methods are available for estimating the radii of certain ions, and the values so determined, taken in conjunction with data from the crystal structures not only of the alkali halides but also of many other compounds, lead to the semi-empirical ionic crystal radii shown in table 3.02 and in fig. 3.05. The interpretation of the radii given in this table is subject to a number of qualifications which will be discussed below. For the present, however, it is sufficient to treat the radii as constant and characteristic of the ions concerned. For the alkali halides with the sodium chloride structure it will be seen that the interatomic distances quoted in table 3.01 are given with fair accuracy as the sum of the corresponding radii from table 3.02. 

---