Van der Waal radius

Since taking simply ionic or van der Waals radii is too crude an approximation, one often rises basis-set-dependent ab initio atomic radii and constnicts the cavity from a set of intersecting spheres centred on the atoms [18, 19], An alternative approach, which is comparatively easy to implement, consists of rising an electrical eqnipotential surface to define the solnte-solvent interface shape [20],... 

The saturation coverage during chemisorption on a clean transition-metal surface is controlled by the fonnation of a chemical bond at a specific site [5] and not necessarily by the area of the molecule. In addition, in this case, the heat of chemisorption of the first monolayer is substantially higher than for the second and subsequent layers where adsorption is via weaker van der Waals interactions. Chemisorption is often usefLil for measuring the area of a specific component of a multi-component surface, for example, the area of small metal particles adsorbed onto a high-surface-area support [6], but not for measuring the total area of the sample. Surface areas measured using this method are specific to the molecule that chemisorbs on the surface. Carbon monoxide titration is therefore often used to define the number of sites available on a supported metal catalyst. In order to measure the total surface area, adsorbates must be selected that interact relatively weakly with the substrate so that the area occupied by each adsorbent is dominated by intennolecular interactions and the area occupied by each molecule is approximately defined by van der Waals radii. This... 

The space filling model developed by Corey, Pauling, and Koltun is also known as the CPK model, or scale model [197], It shows the relative volume (size) of different elements or of different parts of a molecule (Figure 2-123d). The model is based on spheres that represent the "electron cloud . These atomic spheres can be determined from the van der Waals radii (see Section 2.10.1), which indicate the most stable distance between two atoms (non-bonded nuclei). Since the spheres are all drawn to the same scale, the relative size of the overlapping electron clouds of the atoms becomes evident. The connectivities between atoms, the bonds, are not visualized because they are located beneath the atom spheres and are not visible in a non-transparent display (see Section 2.10). In contrast to other models, the CPK model makes it possible to visualize a first impression of the extent of a molecule. 

Non-covalent interactions between molecules often occur at separations where the van der Waals radii of the atoms are just touching and so it is often most useful to examine the electrostatic potential in this region. For this reason, the electrostatic potential is often calculated at the molecular surface (defined in Section 1.5) or the equivalent isodensity surface as shown in Figure 2.18 (colour plate section). Such pictorial representations... 

A yet more realistic cavity shape is that obtained from the van der Waals radii of the atoms of the solute. This is the approach taken in the polarisable continuum method (PCM) [Miertus et al. 1981], which has been implemented in a variety of ab initio and semi-empirical quantu/rt mechanical programs. Due to the non-analytical nature of the cavity shapes in the PCM approach, it is necessary to calculate numerically. The cavity surface is divided... 

The PCM algorithm is as follows. First, the cavity siuface is determined from the van der Waals radii of the atoms. That fraction of each atom s van der Waals sphere which contributes to the cavity is then divided into a nmnber of small surface elements of calculable surface area. The simplest way to to this is to define a local polar coordinate frame at tlie centre of each atom s van der Waals sphere and to use fixed increments of AO and A(p to give rectangular surface elements (Figure 11.22). The surface can also be divided using tessellation methods [Paschual-Ahuir d al. 1987]. An initial value of the point charge for each surface element is then calculated from the electric field gradient due to the solute alone ... 

Fig. 12.20 4-Acetamido benzoic acid. Triangle smoothing predicts that the lower bound distance between the amide nitrogen and the carbonyl oxygen is equal to the sum of the van der Waals radii. The actual distance is about 6.4A.

Alkanes and cycloalkanes are nonpolar and insoluble m water The forces of attraction between alkane molecules are induced dipole/induced dipole attractive forces The boiling points of alkanes increase as the number of carbon atoms increases Branched alkanes have lower boiling points than their unbranched isomers There is a limit to how closely two molecules can approach each other which is given by the sum of their van der Waals radii... 

Nonbonded interactions are the forces be tween atoms that aren t bonded to one another they may be either attractive or repulsive It often happens that the shape of a molecule may cause two atoms to be close in space even though they are sep arated from each other by many bonds Induced dipole/induced dipole interactions make van der Waals forces in alkanes weakly attractive at most distances but when two atoms are closer to each other than the sum of their van der Waals radii nuclear-nuclear and electron-electron repulsive forces between them dominate the fvan derwaais term The resulting destabilization is called van der Waals strain... 

At Its most basic level separating the total strain of a structure into its components is a qualita tive exercise For example a computer drawn model of the eclipsed conformation of butane using ideal bond angles and bond distances (Figure 3 8) reveals that two pairs of hydrogens are separated by a distance of only 175 pm a value considerably smaller than the sum of their van der Waals radii (2 X 120 pm = 240 pm) Thus this conformation is destabilized not only by the torsional strain associ ated with its eclipsed bonds but also by van der Waals strain... 

Van der Waals radius (Section 2 17) A measure of the effec tive size of an atom or a group The repulsive force between two atoms increases rapidly when they approach each other at distances less than the sum of their van der Waals radii Van der Waals strain (Section 3 2) Destabilization that results when two atoms or groups approach each other too closely Also known as van der Waals repulsion Vicinal (Section 6 14) Describing two atoms or groups at tached to adjacent atoms... 

The default exp-6 van der Waals interaction requires, as shown in equation (37) and (38) on page 188, a van der Waals radii, r and a hardness parameter e. The default values for these parameters are based strictly on the atomic number and are given below. 

Figure 4.17 Schematic diagram of bound tyrosine to tyrosyl-tRNA synthetase. Colored regions correspond to van der Waals radii of atoms within a layer of the structure through the tyrosine ring. Red is bound tyrosine green is the end of P strand 2 and the beginning of the following loop region yellow is the loop region 189-192 and brown is part of the a helix in loop region 173-177.

Table 3.1. Van der Waals Radii of Several Atoms and Gronps (A) ...

The haloethanes all have similar rotational barriers of 3.2-3.7 kcal/mol. The increase in the barrier height relative to ethane is probably due to a van der Waals rqjulsive efiect. The heavier halogens have larger van der Waals radii, but this is ofiset by the longer bond lengths, so that the net efiect is a relatively constant rotational barrier for each of the ethyl halides. 

The term "hydrophobic interaction" unfortunately implies some form of molecular repulsion, which, outside the van der Waals radii of a molecule, is quite impossible. The term "hydrophobic force" literally means "fear of water" force. The term hydrophobic has been introduced as an alternative to dispersive but means the same. It is not clear from the literature how the word hydrophobic originated, but it may have been provoked by the immiscibility of a dispersive solvent such as n-heptane with a very polar solvent such as water. 

Van der Waals radius (Section 2.17) A measure of the effective size of an atom or a group. The repulsive force between two atoms increases rapidly when they approach each other at distances less than the sum of their van der Waals radii. 

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