Chapter 2 - Distances

Space-filling models

Van der Waals radii are used to construct a special kind of molecular model called a space-filling model. These models are constructed by drawing each atom as a van der Waals sphere with the atom’s nucleus at the center of the sphere.

Space-filling models are useful because they show how much space an atom (or molecule) occupies. You can see this easily by comparing space-filling models with traditional ball-and-stick models like those in the following figure. The latter do not provide anything like a realistic sense of molecular size.

Ball-and-stick (top) and space-filling models (bottom)




On the other hand, you can also see that it is much harder to establish bond patterns in a space-filling model. Bonds can be located if you recall that bond distances are much smaller than nonbonded distances. A bond must exist between any two atoms that create strongly overlapping spheres.

I mentioned above that van der Waals radii are also used to assess nonbonded interactions. The same kind of assessment can be accomplished using space-filling models. The visual counterpart of a distance “prediction gap” is a model that contains two overlapping nonbonded atoms.

The following figure compares ball-and-stick and space-filling models of three water molecules. The molecules have been positioned so that they occupy roughly the same positions that they might occupy in an ice crystal.

Three water molecules (from ice)

The ball-and-stick model does not reveal much, but the space-filling model clearly shows that the central oxygen atom substantially overlaps with a hydrogen atom in another water molecule. Distance measurements confirm that the nonbonded OH distance (1.8 Å) is much shorter than the sum of the van der Waals radii (1.2 + 1.4 = 2.6 Å).

These observations suggest that water molecules strongly attract each other. This conclusion is supported by some of water’s other strange properties, and chemists have decided that this attractive force deserves a special name. They call it a hydrogen bond. Some scientists claim that water’s hydrogen bonds are responsible for life itself.