Structural Biology Glossary

Van der Waals radii

Since the advent of quantum-mechanics it is well known that atoms are no hard spheres. Their electronic structure has to be described by wavefunctions and the radial part of these wavefunctions is defined between 0 and infinity. When atoms are approachung each other there is an overlap between their electronic wavefunctions and this may lead to various types of interactions. In this respect, the question How large is an atom? makes no sense.

On the other hand, the location of the atomic nuclei are accessible by experimental methods, like X-ray diffraction, for example. One can, for example, very precisely determine that distance d between the two hydrogen atoms in a hydrogen molecule and then conclude that the distance is two times the radius r of a hydrogen atom.

      d
H---------H
    r | r

Starting out from homonuclear interactions one can also derive values for heteronuclear contacts. Due to the very nature of this defintion the radii obtained depend on the type of interaction measured. For example, atom radii obtained from bonded intereactions are definitely different from the corresponding data obtained from non-bonded contacts. Van der Waals radii are determined from contact distances between non-bonded atoms. Comprehensive information on van der Waals radii can be obtained from WebElements. The most common elements in bioploymers (no metals) have the following radii.

Note, that in other compilations slightly different values may be given.
Conversion factors between different units are: 
   1  pm =  1 x 10-12 meter 
 100  pm =  1 Å
 1000 pm =  1 nanometer (nm) 

• Van der Waals radii are used as parameters in mathematical expressions for the empirical description of intermolecular interactions in force fields (Example: Lennard-Jones 12-6 potential:

         Evdw(Rij) = epsilon [(Rij,vdw / Rij )^12) - 2 (Rij,vdw/ Rij )^6].

The first term describes the repulsion and the second one the attraction.

• Severe van der Waals clashes indicate problems with the quality of biopolymer structures. Therefore, many molecular graphics or structure refinement programs have bump check options.
• In spacefilling representations of biopolymers shaded spheres of atoms are shown and often van der Waals radii are adopted for calculating the atom spheres. This type of representation is to simulate the appearence the physical Corey-Pauling-Kolthun (CPK) models. Therefore, ist is often called CPK representation. Here, a representation of a DNA double helix complexed with the drug netropsin is shown (PDB/NDB code: 101d/gdlb31). There are various representations, where either netropsin alone or the complete structure are shown as spacefilling models. This structure of an RNA-protein complex (Glutaminyl-tRNA-synthetase/tRNA complex; PDB/NDB codes: 1gtr/ptr003) is a second example, where again either the complete structure or the RNA or the protein parts are shown in a spacefilling representation.
• The van der Waals radius defines the volume and surface of an atom or molecule. For example, the van der Waals volumes and surfaces of amino acids are given in The Amino Acid Repository.
• Surface representations are useful for exploring the geometrical structure of biopolymeres identifying canyons or clefts or grooves. Obvious examples are the major and minor grooves in nucleic acid double helix structures.

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