Waals radii from crystal structures

Finally we consider interactions between two non-polar atoms or molecules, for instance two noble gas atoms. Their permanent dipole moments are zero, but for a brief fraction of a second the arrangement of electrons in one of them may be such that their centre of gravity does not coincide with the nucleus. The atom will then have an instantaneous dipole moment, and this instantaneous dipole will induce a dipole on the other atom in such a manner that the instantaneous energy is lowered. As time passes, the movement of the electrons in the two atoms is correlated in such a manner that there is a longer-lasting, net lowering of the energy. Such attractive interactions between instantaneous dipoles are referred to as dispersion forces. 

The dispersion interaction increases with the product of the polarizabilities of the two molecules or atoms, and deceases with the distance between them  

We have already noted that the formation of liquids and solids at low temperatures is due to intermolecular attractions. Solid state Ne forms a cubic close-packed lattice each atom is surrounded by 12 nearest neighbors at a distance of 316 pm, about 2% longer than the 7 m distance obtained experimentally by molecular beam studies. The crystal structure of methane at 35 K is also cubic close packed with twelve nearest neighbors at R(C---C) = 416 pm [10] or about 3% longer than the distance of 402 pm. These results indicate that information about the van der Waals radii of atoms may be obtained from the distances 

HOMONUCLEAR DIATOMIC SPECIES OE SECOND-PERIOD ELEMENTS 

Methyl gronp radins 200 Thickness of aromatic ring 170 

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Figure 19-4 contrasts the effective sizes of the halide ions. Each of these dimensions is obtained from the examination of crystal structures of many salts involving the particular halide ion. The effective size found for a given halide ion is called its ionic radius. These radii are larger than the covalent radii but close to the van der Waals radii of neutral atoms. 

The van der Waals radius is defined as a nonbonded distance of closest approach, and these are calculated from the smallest interatomic distances in crystal structures that are considered to be not bonded to one another. Again, these are average values compiled from many crystal structures. If the sum of the van der Waals radii of two adjacent atoms in a structure is greater than the measured distance between them,... 

Covalent bond distances and angles tell us how the atomic nuclei are arranged in space but they do not tell us anything about the outside surfaces of molecules. The distance from the center of an atom to the point at which it contacts an adjacent atom in a packed structure such as a crystal (Fig. 2-1) is known as the van der Waals radius. The ways in which biological molecules fit together are determined largely by the van der Waals contact radii. These, too, are listed in Table 2-1. In every case they are approximately equal to the covalent radius plus 0.08 nm. Van der Waals radii... 

Fig. 6. The water structure in the active site of bovine SOD as obtained from the crystal structure of the reduced enzyme at pH 7.5 (ISXA). The water molecules are represented as spheres of radius corresponding to the van der Waals radius of the oxygen atom, superimposed on the ribbon diagram of the enzyme.

The simple model of an atom as a hard sphere that can approach only to a fixed distance from another atom to which it is not bonded has proved useful in interpreting crystal structures and other molecular properties. The term van der Waals radius, was originally introduced by Pauling as a measure of this atomic size. Thus in a closely packed structure two non-bonded atoms A and B will be separated by the sum of their van der Waals radii (A)... 

To illustrate the solvent effect on the average structure of a protein, we describe results obtained from conventional molecular dynamics simulations with periodic boundary conditions.92,193 This method is well suited for a study of the global features of the structure for which other approaches, such as stochastic boundary simulation methods, would not be appropriate. We consider the bovine pancreatic trypsin inhibitor (BPTI) in solution and in a crystalline environment. A simulation was carried out for a period of 25 ps in the presence of a bath of about 2500 van der Waals particles with a radius and well depth corresponding to that of the oxygen atom in ST2 water.193 The crystal simulation made use of a static crystal environment arising from the surrounding protein molecules in the absence of solvent. These studies, which were the first application of simulation methods to determine the effect of the environment on a protein, used simplified representations of the surround-... 

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