Interatomic contact distances

The structure of iodine at four different pressures. The outlined face-centered unit cell in the 30-Gpa figure corresponds to that of a (distorted) cubic closest-packing of spheres. At 24.6 GPa four unit cells of the face-centered approximant structure are shown the structure is incommensurately modulated, the atomic positions follow a sine wave with a wave length of 3.89 x c. The amplitude of the wave is exaggerated by a factor of two. Lower left Dependence of the twelve interatomic contact distances on pressure... 

Lower left Dependence of the twelve interatomic contact distances on pressure... 

Using a computer and matrix multiplication techniques the first and second peptide units can be rotated through all possible combinations of values of phi and psi. For each possible set of these dihedral angles, the distances between all pairs of nonbonded atoms can be compared using a set of minimum interatomic contact distances (Table 2.3) if the distance between any set of atoms is smaller than the minimum contact distance then that conformation is not allowed. This boils down to the fact that two atoms cannot be closer than the sum of the van der Waals radii of each atom or electron repulsion occurs. Therefore, by determining the values of phi and... 

When two atoms approach each other so closely that their electron clouds interpenetrate, strong repulsion occurs. Such repulsive van der Waals forces follow an inverse 12th-power dependence on r (1/r ), as shown in Figure 1.13. Between the repulsive and attractive domains lies a low point in the potential curve. This low point defines the distance known as the van der Waals contact distance, which is the interatomic distance that results if only van der Waals forces hold two atoms together. The limit of approach of two atoms is determined by the sum of their van der Waals radii (Table 1.4). 

A reduced strain parameter is then defined with reference to an arbitrarily selected set of contacts. With reference to the dx distances the strain parameter may be defined as . S = (Dx — dx)/DY. This parameter gives an indication of the atomic dimension compression. It is computed, as a function of the ratio e = DX/DY = Rx/Ry, for the different kinds of interatomic contact. 

The interatomic distance at the bottom of the potential well, the most favorable distance of separation, is known as the van der Waals contact distance. A particular atom has a characteristic van der Waals radius (Table 11.3). These radii are additive, so that the optimal distance of contact between two atoms may be found by the addition of their two van der Waals radii. The van der Waals radii are not as sharply defined as covalent bond radii. This is because the potential energy wells are so shallow that contact distances may vary by 0.1 A (0.01 nm) or so... 

Equation (2.2.12) may be directly obtained from minimizing the elastic free energy under the constraint that the mean-square radius of gyration has a fixed value [see Eqs. (2.1.63) and (2.1.39), C q) -+ ot q)C q) [10]. The physical meaning of this result is that under chain compression the free energy due to the interatomic contacts is basically a function of only, no matter what are the individual values of the a (q). As a consequence, all the mean-square distances (r (k)) may be expressed under a general form [53]. Defining... 

At room temperature, solid [Pt(bph)(CO)2] 26 (H2bph=biphenyl) displays an intense and broad emission at 726 nm [33]. As described in earlier report [34], [Pt(bph)(CO)2] packs in a columnar structure with Pt-Pt distances of 3.24 A. Such close interatomic contacts in the chain packing of square planar platinum(II) complexes always impart red-shifts in their emission spectra. The emission maximum is red-shifted to 791 nm upon decreasing the temperature from 296 to 77 K, which is consistent with a decrease in the Pt-Pt separation observed by Connick [35] and Yersin [3a]. 

In Appendix A published tables of standard interatomic distances [4] are reproduced in slightly abbreviated form. We have limited ourselves to a selection of the more reliable standards, those based on at least four observed distances for the type of interatomic contact in question for the others the reader is referred to the original tables [4]. Appendix B gives database identification codes (refcodes) to crys-... 

Crystallographic literature is full of information on the so-called close interatomic contacts, which in the case of distances between H-atoms and electron donating atoms are used as a criterion of H-bond existence. If this distance is shorter than the sum of van der Waals radii - then the H-bond type interaction is assumed... 

As indicated, an implicit assumption of the JKR theory is that there are no interactions outside the contact radius. More specifically, the energy arguments used in the development of the JKR theory do not allow specific locations of the adhesion forces to be determined except that they must be associated with the contact line where the two surfaces of the particle and substrate become joined. Adhesion-induced stresses act at the surface and not a result of action-at-a-distance interatomic forces. This results in a stress singularity at the circumference of the contact radius [41]. The validity of this assumption was first questioned by Derjaguin et al. [42], who proposed an alternative model of adhesion (commonly referred to as the DMT theory ). Needless to say, the predictions of the JKR and DMT models are vastly different, as discussed by Tabor [41]. 

Structures of some polycations. Interatomic distances in pm. Short contacts... 

The compounds [Fe(C5Me4SCMe3)2][M(mnt)2] (M = Ni, Pt) are the only cases of salts based on metallocenium derivatives and on [M(mnt)2 complexes where the crystal structure is based in parallel arrangements of the type I chain motif [49]. In the chains the [Pt(mnt)2]- units are considerably tilted in relation to the chain direction, and short interatomic D+A- intrachain contacts were observed, involving one C from the Cp and a S atom from the anion, with a C-S distance of the order of dtf/. Relatively short interchain interionic distances were observed, where the closest corresponds to a S... C, involving one S atom from the anion and a C atom from a Me group of the cation, exceeding dw by 10%. 

The crystal structure of [Fe(Cp )2][Ni(bds)2], as the salts described in Sect. 3.4.1, consists of 2D layers composed of parallel type IVa chains, which are separated by anion layers [15]. Besides contacts involving H atoms, no other short contacts were found in the structure. Within the IVa chains, one of the Cp fragments of the cation sits above a C6 ring of the ligand, while the second one is displaced towards the center of the anion. For the first Cp the closest D+A interatomic separation (C C) exceeds dw by 8%, while for the second Cp the closest D+A contact (C—Se) exceeds c/w by 4%. The D+D+A chains are relatively isolated and the solvent is located on cavities between the chains. No close interionic interlayer distances were observed involving molecules in the D+D+A layers and the anion layers or between the anions in the anionic layers. 

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