Van der Waals’ distance

Figure 2-117. Dependence of the van der Waals energy on the distance between two non-con-nected atom nuclei. With decreasing atoiTiic distance the energy between the two atoms becomes attraction, going through a minimum at the van der Waals distance. Then, upon a further decrease in the distance, a rapid increase in repulsion energy is observed.

Secondly, at an initial stage, the first layer of C2 units diffusing out of the catalyst remains at a Van der Waals distance from the C, layer coordinated to the catalyst surface. Then, if the units of that outer layer bind to one another, this will lead to a half fullerene. Depending on whether the central axis of that half fullerene is a threefold or a fivefold rotation axis, a (9n,0) or a (5n,5 ) tubule will start growing, respectively. The half fullerene can also grow to completion instead of starting a nanotu-bule[ 17]. This assumption is reinforced by the fact that we have detected, by HPLC and mass spectrometry, the presence of fullerenes Qo, C70,. .. 

The van der Waals distance, Rq, and softness parameters, depend on both atom types. These parameters are in all force fields written in terms of parameters for the individual atom types. There are several ways of combining atomic parameters to diatomic parameters, some of them being quite complicated. A commonly used method is to take the van der Waals minimum distance as the sum of two van der Waals radii, and the interaction parameter as the geometrical mean of atomic softness constants. 

Finds the smallest distance between the solute and the grid points. Checks if the given grid point is within the van der waals distance from I any of the solute atoms. 

Calculate the halogen-halogen distances and compare them with the VAN DER WAALS distances. What do you conclude ... 

The molecules in crystalline chlorine, bromine and iodine are packed in a different manner, as shown in Fig. 11.1. The rather different distances between atoms of adjacent molecules are remarkable. If we take the van der Waals distance, such as observed in organic and inorganic molecular compounds, as reference, then some of the intermolecular contacts in the b-c plane are shorter, whereas they are longer to the molecules of the next plane. We thus observe a certain degree of association of the halogen molecules within the b-c plane (dotted in Fig. 11.1, top left). This association increases from chlorine to iodine. The weaker attractive forces between the planes show up in the plate-like habit of the crystals and in their easy cleavage parallel to the layers. Similar association tendencies are also observed for the heavier elements of the fifth and sixth main groups. 

Tellurium crystallizes isotypic to a-selenium. As expected, the Te-Te bonds in the chain (283 pm) are longer than in selenium, but the contact distances to the atoms of the adjacent chains are nearly the same (Te- Te 349 pm). The shortening, as compared to the van der Waals distance, is more marked and the deviation from a regular octahedral coordination of the atoms is reduced (cf. Table 11.1, p. 111). By exerting pressure all six distances can be made to be equal (cf. Section 11.4). 

Arsenic modifications with the structures of white and black phosphorus have been described. However, only gray (metallic, rhombohedral) a-arsenic is stable. It consists of layers of six-membered rings in the chair conformation that are connected with each other in the same way as in /ran.v-dccalin (Fig. 11.7). In the layer the atoms are situated alternately in an upper and a lower plane. The layers are stacked in a staggered manner such that over and under the center of every ring there is an As atom in an adjacent layer. In this way every As atom is in contact with three more atoms in addition to the three atoms to which it is bonded within the layer it has a distorted octahedral 3 + 3 coordination. The As-As bond length in the layer is 252 pm the distance between adjacent atoms of different layers is 312 pm and thus is considerably shorter than the van der Waals distance (370 pm). 

Structures of some polyiodides. The I2 building units are in bold face. Bond lengths in pm. For comparison molecule I—I 268 pm, VAN DER Waals distance L 1396 pm... 

Photolyzing with UV light may result in immediate reaction of the nitrene intermediate with a target molecule within Van der Waals distance, or may result in ring expansion to the nucleophile-reactive dehydroazepine. The ring-expanded product is reactive primarily with amine groups (Figure 5.31). 

Processes accompanied by a decrease in volume, such as C—C bond formation, in which the distance between two carbon atoms decreases from the van der Waals distance of ca 3.6 A to the bonding distance of ca 1.5 A, are accelerated by raising the pressure and equilibria are shifted toward the side of products (AV < 0, AV < 0). The reverse reaction, a homolytic bond cleavage, leads to an increase in volume (AV / > 0, AV > 0). Pressure induces a deceleration of such a process and a shift in equilibrium toward the side of reactants. However, in an ionization, such as an ionic dissociation, the attractive interaction between the ions generated and the solvent molecules leads to a contraction... 

The close-packing principle implies that the energy minima are close to the minima of the multidimensional volume surface, provided that the distances between neighboring atoms of different molecules are not lower than the van der Waals distances. 

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