Van der Walls radii

Fig. 3.1. Visualization of a drug molecule N-(4-hydroxy-phenyl)-acetamide (Tylenol or acetaminophen) computerized with different levels of graphic representations. (A) Molecular structure of the drug Tylenol. (B) Ball-stick model showing atomic positions and types. (C) Ball-stick model with van der Waals dot surfaces. (D) Space-filled model showing van der Walls radii of the oxygen, nitrogen, and carbon atoms. (E) Solvent accessible surface model (solid) (solvent radius, 1.4A). (See black and white image.)...

Packing diagram for ampicillin trihydrate deduced from the single crystal stractural data. The van der Walls radii are included for the water hydrogens and oxygen, and the channels are along the screw axes. 

In Nature, atoms are located at different interatomic distances depending on a kind of the forces between them either by cohesion forces or chemical bonds. The latter prevail at the distances which are smaller or equal to the sum of van der Waals radii of atoms. At such distances atoms form a molecule. By definition, the van der Waals (vdW) radii of a given atom is the half of the shortest distance that is observed in crystals between the nuclei of the same atoms. The vdW radii of atoms are listed in Table 1. At the distances beymid the sum of van der Waals radii of atoms, there exists a specific van der Waals interaction often referred to as the dispersion interaction between atoms, after Johannes Diderik van der Waals who first postulated its existence in his well-known equation of state derived in his PhD thesis in 1837 and which won him the 1910 Nobel Prize in Physics. For the first time van der Waals explained the deviations of gases from the ideal behavior. Let us consider a vessel filled by a gas of atoms. Within this vessel, the pressure exerted by a gas of atoms on its wall is lower compared to that predicted by the ideal gas law since the atoms may collide with the wall and are thus retained by the attraction they undergo from the other atoms in the bulk of the gas that results in the pressure P obeying the equation [94],... 

In this algorithm, an initial random position is chosen inside the pore network and at any given distance along the pore axis. Pore sizes are evaluated by calculating the maximum size for a spherical probe to still fit in the pore without overlapping with van der Waals radii of beads in the pore wall. 

It would be of practical importance to know how close two molecules can be to each other. We will not entertain this question too seriously, though, because this problem cannot have an elegant solution it depends on the direction of the approach and the atoms involved, as well as how strongly the two molecules collide. Searching for the effective radii of atoms would be nonsense, if the valence repulsion were not a sort of soft wall or if the atom sizes were very sensitive to molecular details. Fortunately, it turns out that an atom, despite different roles played in molecules, can be characterized by its approximate radius, called the van der Waals radius. The radius may be determined in a naive but quite effective way. For example, we may approach two HF molecules like that H-F...F-H, axially with the fluorine atoms heading on, then find the distance Rff which the interaction energy is equal to, say, 5 kcals/mol. The proposed fluorine atom radius would be A similar procedure may be repeated with... 

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